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# Applied Machine Learning: Module 3 (Evaluation)

## Evaluation for Classification

### Preamble

``````

In [1]:

%matplotlib notebook
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split

X, y = dataset.data, dataset.target

for class_name, class_count in zip(dataset.target_names, np.bincount(dataset.target)):
print(class_name,class_count)

``````
``````

0 178
1 182
2 177
3 183
4 181
5 182
6 181
7 179
8 174
9 180

``````
``````

In [2]:

# Creating a dataset with imbalanced binary classes:
# Negative class (0) is 'not digit 1'
# Positive class (1) is 'digit 1'
y_binary_imbalanced = y.copy()
y_binary_imbalanced[y_binary_imbalanced != 1] = 0

print('Original labels:\t', y[1:30])
print('New binary labels:\t', y_binary_imbalanced[1:30])

``````
``````

Original labels:	 [1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9]
New binary labels:	 [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]

``````
``````

In [3]:

np.bincount(y_binary_imbalanced)    # Negative class (0) is the most frequent class

``````
``````

Out[3]:

array([1615,  182])

``````
``````

In [4]:

X_train, X_test, y_train, y_test = train_test_split(X, y_binary_imbalanced, random_state=0)

# Accuracy of Support Vector Machine classifier
from sklearn.svm import SVC

svm = SVC(kernel='rbf', C=1).fit(X_train, y_train)
svm.score(X_test, y_test)

``````
``````

Out[4]:

0.90888888888888886

``````

### Dummy Classifiers

DummyClassifier is a classifier that makes predictions using simple rules, which can be useful as a baseline for comparison against actual classifiers, especially with imbalanced classes.

``````

In [5]:

from sklearn.dummy import DummyClassifier

# Negative class (0) is most frequent
dummy_majority = DummyClassifier(strategy = 'most_frequent').fit(X_train, y_train)
# Therefore the dummy 'most_frequent' classifier always predicts class 0
y_dummy_predictions = dummy_majority.predict(X_test)

y_dummy_predictions

``````
``````

Out[5]:

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

``````
``````

In [6]:

dummy_majority.score(X_test, y_test)

``````
``````

Out[6]:

0.9044444444444445

``````
``````

In [7]:

svm = SVC(kernel='linear', C=1).fit(X_train, y_train)
svm.score(X_test, y_test)

``````
``````

Out[7]:

0.97777777777777775

``````

### Confusion matrices

#### Binary (two-class) confusion matrix

``````

In [8]:

from sklearn.metrics import confusion_matrix

# Negative class (0) is most frequent
dummy_majority = DummyClassifier(strategy = 'most_frequent').fit(X_train, y_train)
y_majority_predicted = dummy_majority.predict(X_test)
confusion = confusion_matrix(y_test, y_majority_predicted)

print('Most frequent class (dummy classifier)\n', confusion)

``````
``````

Most frequent class (dummy classifier)
[[407   0]
[ 43   0]]

``````
``````

In [9]:

# produces random predictions w/ same class proportion as training set
dummy_classprop = DummyClassifier(strategy='stratified').fit(X_train, y_train)
y_classprop_predicted = dummy_classprop.predict(X_test)
confusion = confusion_matrix(y_test, y_classprop_predicted)

print('Random class-proportional prediction (dummy classifier)\n', confusion)

``````
``````

Random class-proportional prediction (dummy classifier)
[[372  35]
[ 38   5]]

``````
``````

In [10]:

svm = SVC(kernel='linear', C=1).fit(X_train, y_train)
svm_predicted = svm.predict(X_test)
confusion = confusion_matrix(y_test, svm_predicted)

print('Support vector machine classifier (linear kernel, C=1)\n', confusion)

``````
``````

Support vector machine classifier (linear kernel, C=1)
[[402   5]
[  5  38]]

``````
``````

In [11]:

from sklearn.linear_model import LogisticRegression

lr = LogisticRegression().fit(X_train, y_train)
lr_predicted = lr.predict(X_test)
confusion = confusion_matrix(y_test, lr_predicted)

print('Logistic regression classifier (default settings)\n', confusion)

``````
``````

Logistic regression classifier (default settings)
[[401   6]
[  6  37]]

``````
``````

In [12]:

from sklearn.tree import DecisionTreeClassifier

dt = DecisionTreeClassifier(max_depth=2).fit(X_train, y_train)
tree_predicted = dt.predict(X_test)
confusion = confusion_matrix(y_test, tree_predicted)

print('Decision tree classifier (max_depth = 2)\n', confusion)

``````
``````

Decision tree classifier (max_depth = 2)
[[400   7]
[ 17  26]]

``````

### Evaluation metrics for binary classification

``````

In [13]:

from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
# Accuracy = TP + TN / (TP + TN + FP + FN)
# Precision = TP / (TP + FP)
# Recall = TP / (TP + FN)  Also known as sensitivity, or True Positive Rate
# F1 = 2 * Precision * Recall / (Precision + Recall)
print('Accuracy: {:.2f}'.format(accuracy_score(y_test, tree_predicted)))
print('Precision: {:.2f}'.format(precision_score(y_test, tree_predicted)))
print('Recall: {:.2f}'.format(recall_score(y_test, tree_predicted)))
print('F1: {:.2f}'.format(f1_score(y_test, tree_predicted)))

``````
``````

Accuracy: 0.95
Precision: 0.79
Recall: 0.60
F1: 0.68

``````
``````

In [14]:

# Combined report with all above metrics
from sklearn.metrics import classification_report

print(classification_report(y_test, tree_predicted, target_names=['not 1', '1']))

``````
``````

precision    recall  f1-score   support

not 1       0.96      0.98      0.97       407
1       0.79      0.60      0.68        43

avg / total       0.94      0.95      0.94       450

``````
``````

In [15]:

print('Random class-proportional (dummy)\n',
classification_report(y_test, y_classprop_predicted, target_names=['not 1', '1']))
print('SVM\n',
classification_report(y_test, svm_predicted, target_names = ['not 1', '1']))
print('Logistic regression\n',
classification_report(y_test, lr_predicted, target_names = ['not 1', '1']))
print('Decision tree\n',
classification_report(y_test, tree_predicted, target_names = ['not 1', '1']))

``````
``````

Random class-proportional (dummy)
precision    recall  f1-score   support

not 1       0.91      0.91      0.91       407
1       0.12      0.12      0.12        43

avg / total       0.83      0.84      0.84       450

SVM
precision    recall  f1-score   support

not 1       0.99      0.99      0.99       407
1       0.88      0.88      0.88        43

avg / total       0.98      0.98      0.98       450

Logistic regression
precision    recall  f1-score   support

not 1       0.99      0.99      0.99       407
1       0.86      0.86      0.86        43

avg / total       0.97      0.97      0.97       450

Decision tree
precision    recall  f1-score   support

not 1       0.96      0.98      0.97       407
1       0.79      0.60      0.68        43

avg / total       0.94      0.95      0.94       450

``````

### Decision functions

``````

In [16]:

X_train, X_test, y_train, y_test = train_test_split(X, y_binary_imbalanced, random_state=0)
y_scores_lr = lr.fit(X_train, y_train).decision_function(X_test)
y_score_list = list(zip(y_test[0:20], y_scores_lr[0:20]))

# show the decision_function scores for first 20 instances
y_score_list

``````
``````

Out[16]:

[(0, -23.172292973469546),
(0, -13.542576515500063),
(0, -21.717588760007867),
(0, -18.903065133316439),
(0, -19.733169947138638),
(0, -9.7463217496747667),
(1, 5.2327155658831135),
(0, -19.308012306288916),
(0, -25.099330209728528),
(0, -21.824312362996),
(0, -24.14378275072049),
(0, -19.578811099762508),
(0, -22.568371393280199),
(0, -10.822590225240777),
(0, -11.907918741521932),
(0, -10.977026853802803),
(1, 11.206811164226373),
(0, -27.64415761980748),
(0, -12.857692102545409),
(0, -25.848149140240199)]

``````
``````

In [17]:

X_train, X_test, y_train, y_test = train_test_split(X, y_binary_imbalanced, random_state=0)
y_proba_lr = lr.fit(X_train, y_train).predict_proba(X_test)
y_proba_list = list(zip(y_test[0:20], y_proba_lr[0:20,1]))

# show the probability of positive class for first 20 instances
y_proba_list

``````
``````

Out[17]:

[(0, 8.6377579220606777e-11),
(0, 1.3138118599563783e-06),
(0, 3.6997386039099529e-10),
(0, 6.1730972504865465e-09),
(0, 2.6914925394345074e-09),
(0, 5.8506057771143608e-05),
(1, 0.99468934644404694),
(0, 4.1175302368500096e-09),
(0, 1.2574750894253029e-11),
(0, 3.3252290754668869e-10),
(0, 3.2695529799373086e-11),
(0, 3.1407283576084884e-09),
(0, 1.5800864117150149e-10),
(0, 1.9943442430612578e-05),
(0, 6.7368003023860014e-06),
(0, 1.7089540581641637e-05),
(1, 0.9999864188091131),
(0, 9.8694940340195476e-13),
(0, 2.6059983600823893e-06),
(0, 5.9469113009063784e-12)]

``````

### Precision-recall curves

``````

In [18]:

from sklearn.metrics import precision_recall_curve

precision, recall, thresholds = precision_recall_curve(y_test, y_scores_lr)
closest_zero = np.argmin(np.abs(thresholds))
closest_zero_p = precision[closest_zero]
closest_zero_r = recall[closest_zero]

plt.figure()
plt.xlim([0.0, 1.01])
plt.ylim([0.0, 1.01])
plt.plot(precision, recall, label='Precision-Recall Curve')
plt.plot(closest_zero_p, closest_zero_r, 'o', markersize = 12, fillstyle = 'none', c='r', mew=3)
plt.xlabel('Precision', fontsize=16)
plt.ylabel('Recall', fontsize=16)
plt.axes().set_aspect('equal')
plt.show()

``````
``````

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mpl.get_websocket_type = function() {
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return MozWebSocket;
} else {
'Please try Chrome, Safari or Firefox ≥ 6. ' +
'Firefox 4 and 5 are also supported but you ' +
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};
}

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warnings.textContent = (
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this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

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mpl.figure.prototype._canvas_extra_style = function(canvas_div) {

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mpl.figure.prototype._root_extra_style = function(canvas_div) {

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mpl.figure.prototype._init_canvas = function() {
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mpl.figure.prototype.handle_save = function(fig, msg) {
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mpl.figure.prototype.handle_resize = function(fig, msg) {
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mpl.figure.prototype.handle_rubberband = function(fig, msg) {
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x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
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fig.rubberband_context.strokeRect(min_x, min_y, width, height);
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mpl.figure.prototype.handle_figure_label = function(fig, msg) {
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mpl.figure.prototype.handle_cursor = function(fig, msg) {
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mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
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mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - \$(targ).offset().left;
var y = e.pageY - \$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overriden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = \$("#" + id);

window.open(figure.imageObj.src);
}

var fig = new mpl.figure(id, ws_proxy,
element.get(0));

// Call onopen now - mpl needs it, as it is assuming we've passed it a real
// web socket which is closed, not our websocket->open comm proxy.
ws_proxy.onopen();

fig.parent_element = element.get(0);
fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>");
if (!fig.cell_info) {
console.error("Failed to find cell for figure", id, fig);
return;
}

var output_index = fig.cell_info[2]
var cell = fig.cell_info[0];

};

mpl.figure.prototype.handle_close = function(fig, msg) {
var width = fig.canvas.width/mpl.ratio
fig.root.unbind('remove')

// Update the output cell to use the data from the current canvas.
fig.push_to_output();
var dataURL = fig.canvas.toDataURL();
// Re-enable the keyboard manager in IPython - without this line, in FF,
// the notebook keyboard shortcuts fail.
IPython.keyboard_manager.enable()
\$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items){
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) { continue; };

var button = \$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = \$('<span class="mpl-message" style="text-align:right; float: right;"/>');
nav_element.append(status_bar);
this.message = status_bar[0];

// Add the close button to the window.
var buttongrp = \$('<div class="btn-group inline pull-right"></div>');
var button = \$('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>');
button.click(function (evt) { fig.handle_close(fig, {}); } );
button.mouseover('Stop Interaction', toolbar_mouse_event);
buttongrp.append(button);
var titlebar = this.root.find(\$('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
// select the cell after this one
var index = IPython.notebook.find_cell_index(this.cell_info[0]);
IPython.notebook.select(index + 1);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}

``````

### ROC curves, Area-Under-Curve (AUC)

``````

In [19]:

from sklearn.metrics import roc_curve, auc

X_train, X_test, y_train, y_test = train_test_split(X, y_binary_imbalanced, random_state=0)

y_score_lr = lr.fit(X_train, y_train).decision_function(X_test)
fpr_lr, tpr_lr, _ = roc_curve(y_test, y_score_lr)
roc_auc_lr = auc(fpr_lr, tpr_lr)

plt.figure()
plt.xlim([-0.01, 1.00])
plt.ylim([-0.01, 1.01])
plt.plot(fpr_lr, tpr_lr, lw=3, label='LogRegr ROC curve (area = {:0.2f})'.format(roc_auc_lr))
plt.xlabel('False Positive Rate', fontsize=16)
plt.ylabel('True Positive Rate', fontsize=16)
plt.title('ROC curve (1-of-10 digits classifier)', fontsize=16)
plt.legend(loc='lower right', fontsize=13)
plt.plot([0, 1], [0, 1], color='navy', lw=3, linestyle='--')
plt.axes().set_aspect('equal')
plt.show()

``````
``````

var element = \$('#e417b6d4-a0d2-4124-8756-e9a11f7eb774');
/* Put everything inside the global mpl namespace */
window.mpl = {};

mpl.get_websocket_type = function() {
if (typeof(WebSocket) !== 'undefined') {
return WebSocket;
} else if (typeof(MozWebSocket) !== 'undefined') {
return MozWebSocket;
} else {
'Please try Chrome, Safari or Firefox ≥ 6. ' +
'Firefox 4 and 5 are also supported but you ' +
'have to enable WebSockets in about:config.');
};
}

this.id = figure_id;

this.ws = websocket;

this.supports_binary = (this.ws.binaryType != undefined);

if (!this.supports_binary) {
var warnings = document.getElementById("mpl-warnings");
if (warnings) {
warnings.style.display = 'block';
warnings.textContent = (
"This browser does not support binary websocket messages. " +
"Performance may be slow.");
}
}

this.imageObj = new Image();

this.context = undefined;
this.message = undefined;
this.canvas = undefined;
this.rubberband_canvas = undefined;
this.rubberband_context = undefined;
this.format_dropdown = undefined;

this.image_mode = 'full';

this.root = \$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

\$(parent_element).append(this.root);

this._init_canvas(this);
this._init_toolbar(this);

var fig = this;

this.waiting = false;

this.ws.onopen =  function () {
fig.send_message("supports_binary", {value: fig.supports_binary});
fig.send_message("send_image_mode", {});
if (mpl.ratio != 1) {
fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio});
}
fig.send_message("refresh", {});
}

if (fig.image_mode == 'full') {
// Full images could contain transparency (where diff images
// almost always do), so we need to clear the canvas so that
// there is no ghosting.
fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);
}
fig.context.drawImage(fig.imageObj, 0, 0);
};

this.ws.close();
}

this.ws.onmessage = this._make_on_message_function(this);

}

var titlebar = \$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = \$(
'<div class="ui-dialog-title" style="width: 100%; ' +
titlebar.append(titletext)
this.root.append(titlebar);
}

mpl.figure.prototype._canvas_extra_style = function(canvas_div) {

}

mpl.figure.prototype._root_extra_style = function(canvas_div) {

}

mpl.figure.prototype._init_canvas = function() {
var fig = this;

var canvas_div = \$('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = \$('<canvas/>');
canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0")

this.canvas = canvas[0];
this.context = canvas[0].getContext("2d");

var backingStore = this.context.backingStorePixelRatio ||
this.context.webkitBackingStorePixelRatio ||
this.context.mozBackingStorePixelRatio ||
this.context.msBackingStorePixelRatio ||
this.context.oBackingStorePixelRatio ||
this.context.backingStorePixelRatio || 1;

mpl.ratio = (window.devicePixelRatio || 1) / backingStore;

var rubberband = \$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
return false;
});

function set_focus () {
canvas.focus();
canvas_div.focus();
}

window.setTimeout(set_focus, 100);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = \$('<button/>');
button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +
'ui-button-icon-only');
button.attr('role', 'button');
button.attr('aria-disabled', 'false');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);

var icon_img = \$('<span/>');

var tooltip_span = \$('<span/>');
tooltip_span.html(tooltip);

button.append(icon_img);
button.append(tooltip_span);

nav_element.append(button);
}

var fmt_picker_span = \$('<span/>');

var fmt_picker = \$('<select/>');
fmt_picker_span.append(fmt_picker);
nav_element.append(fmt_picker_span);
this.format_dropdown = fmt_picker[0];

for (var ind in mpl.extensions) {
var fmt = mpl.extensions[ind];
var option = \$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}

// Add hover states to the ui-buttons
\$( ".ui-button" ).hover(
function() { \$(this).removeClass("ui-state-hover");}
);

var status_bar = \$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - \$(targ).offset().left;
var y = e.pageY - \$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overriden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = \$("#" + id);

window.open(figure.imageObj.src);
}

var fig = new mpl.figure(id, ws_proxy,
element.get(0));

// Call onopen now - mpl needs it, as it is assuming we've passed it a real
// web socket which is closed, not our websocket->open comm proxy.
ws_proxy.onopen();

fig.parent_element = element.get(0);
fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>");
if (!fig.cell_info) {
console.error("Failed to find cell for figure", id, fig);
return;
}

var output_index = fig.cell_info[2]
var cell = fig.cell_info[0];

};

mpl.figure.prototype.handle_close = function(fig, msg) {
var width = fig.canvas.width/mpl.ratio
fig.root.unbind('remove')

// Update the output cell to use the data from the current canvas.
fig.push_to_output();
var dataURL = fig.canvas.toDataURL();
// Re-enable the keyboard manager in IPython - without this line, in FF,
// the notebook keyboard shortcuts fail.
IPython.keyboard_manager.enable()
\$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items){
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) { continue; };

var button = \$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = \$('<span class="mpl-message" style="text-align:right; float: right;"/>');
nav_element.append(status_bar);
this.message = status_bar[0];

// Add the close button to the window.
var buttongrp = \$('<div class="btn-group inline pull-right"></div>');
var button = \$('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>');
button.click(function (evt) { fig.handle_close(fig, {}); } );
button.mouseover('Stop Interaction', toolbar_mouse_event);
buttongrp.append(button);
var titlebar = this.root.find(\$('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
// select the cell after this one
var index = IPython.notebook.find_cell_index(this.cell_info[0]);
IPython.notebook.select(index + 1);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}

``````
``````

In [20]:

from matplotlib import cm

X_train, X_test, y_train, y_test = train_test_split(X, y_binary_imbalanced, random_state=0)

plt.figure()
plt.xlim([-0.01, 1.00])
plt.ylim([-0.01, 1.01])
for g in [0.01, 0.1, 0.20, 1]:
svm = SVC(gamma=g).fit(X_train, y_train)
y_score_svm = svm.decision_function(X_test)
fpr_svm, tpr_svm, _ = roc_curve(y_test, y_score_svm)
roc_auc_svm = auc(fpr_svm, tpr_svm)
accuracy_svm = svm.score(X_test, y_test)
print("gamma = {:.2f}  accuracy = {:.2f}   AUC = {:.2f}".format(g, accuracy_svm,
roc_auc_svm))
plt.plot(fpr_svm, tpr_svm, lw=3, alpha=0.7,
label='SVM (gamma = {:0.2f}, area = {:0.2f})'.format(g, roc_auc_svm))

plt.xlabel('False Positive Rate', fontsize=16)
plt.ylabel('True Positive Rate (Recall)', fontsize=16)
plt.plot([0, 1], [0, 1], color='k', lw=0.5, linestyle='--')
plt.legend(loc="lower right", fontsize=11)
plt.title('ROC curve: (1-of-10 digits classifier)', fontsize=16)
plt.axes().set_aspect('equal')

plt.show()

``````
``````

var element = \$('#867ea8d1-6b04-4bcf-b6fd-9e0e6b15017d');
/* Put everything inside the global mpl namespace */
window.mpl = {};

mpl.get_websocket_type = function() {
if (typeof(WebSocket) !== 'undefined') {
return WebSocket;
} else if (typeof(MozWebSocket) !== 'undefined') {
return MozWebSocket;
} else {
'Please try Chrome, Safari or Firefox ≥ 6. ' +
'Firefox 4 and 5 are also supported but you ' +
'have to enable WebSockets in about:config.');
};
}

this.id = figure_id;

this.ws = websocket;

this.supports_binary = (this.ws.binaryType != undefined);

if (!this.supports_binary) {
var warnings = document.getElementById("mpl-warnings");
if (warnings) {
warnings.style.display = 'block';
warnings.textContent = (
"This browser does not support binary websocket messages. " +
"Performance may be slow.");
}
}

this.imageObj = new Image();

this.context = undefined;
this.message = undefined;
this.canvas = undefined;
this.rubberband_canvas = undefined;
this.rubberband_context = undefined;
this.format_dropdown = undefined;

this.image_mode = 'full';

this.root = \$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

\$(parent_element).append(this.root);

this._init_canvas(this);
this._init_toolbar(this);

var fig = this;

this.waiting = false;

this.ws.onopen =  function () {
fig.send_message("supports_binary", {value: fig.supports_binary});
fig.send_message("send_image_mode", {});
if (mpl.ratio != 1) {
fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio});
}
fig.send_message("refresh", {});
}

if (fig.image_mode == 'full') {
// Full images could contain transparency (where diff images
// almost always do), so we need to clear the canvas so that
// there is no ghosting.
fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);
}
fig.context.drawImage(fig.imageObj, 0, 0);
};

this.ws.close();
}

this.ws.onmessage = this._make_on_message_function(this);

}

var titlebar = \$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = \$(
'<div class="ui-dialog-title" style="width: 100%; ' +
titlebar.append(titletext)
this.root.append(titlebar);
}

mpl.figure.prototype._canvas_extra_style = function(canvas_div) {

}

mpl.figure.prototype._root_extra_style = function(canvas_div) {

}

mpl.figure.prototype._init_canvas = function() {
var fig = this;

var canvas_div = \$('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = \$('<canvas/>');
canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0")

this.canvas = canvas[0];
this.context = canvas[0].getContext("2d");

var backingStore = this.context.backingStorePixelRatio ||
this.context.webkitBackingStorePixelRatio ||
this.context.mozBackingStorePixelRatio ||
this.context.msBackingStorePixelRatio ||
this.context.oBackingStorePixelRatio ||
this.context.backingStorePixelRatio || 1;

mpl.ratio = (window.devicePixelRatio || 1) / backingStore;

var rubberband = \$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
return false;
});

function set_focus () {
canvas.focus();
canvas_div.focus();
}

window.setTimeout(set_focus, 100);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = \$('<button/>');
button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +
'ui-button-icon-only');
button.attr('role', 'button');
button.attr('aria-disabled', 'false');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);

var icon_img = \$('<span/>');

var tooltip_span = \$('<span/>');
tooltip_span.html(tooltip);

button.append(icon_img);
button.append(tooltip_span);

nav_element.append(button);
}

var fmt_picker_span = \$('<span/>');

var fmt_picker = \$('<select/>');
fmt_picker_span.append(fmt_picker);
nav_element.append(fmt_picker_span);
this.format_dropdown = fmt_picker[0];

for (var ind in mpl.extensions) {
var fmt = mpl.extensions[ind];
var option = \$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}

// Add hover states to the ui-buttons
\$( ".ui-button" ).hover(
function() { \$(this).removeClass("ui-state-hover");}
);

var status_bar = \$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - \$(targ).offset().left;
var y = e.pageY - \$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overriden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = \$("#" + id);

window.open(figure.imageObj.src);
}

var fig = new mpl.figure(id, ws_proxy,
element.get(0));

// Call onopen now - mpl needs it, as it is assuming we've passed it a real
// web socket which is closed, not our websocket->open comm proxy.
ws_proxy.onopen();

fig.parent_element = element.get(0);
fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>");
if (!fig.cell_info) {
console.error("Failed to find cell for figure", id, fig);
return;
}

var output_index = fig.cell_info[2]
var cell = fig.cell_info[0];

};

mpl.figure.prototype.handle_close = function(fig, msg) {
var width = fig.canvas.width/mpl.ratio
fig.root.unbind('remove')

// Update the output cell to use the data from the current canvas.
fig.push_to_output();
var dataURL = fig.canvas.toDataURL();
// Re-enable the keyboard manager in IPython - without this line, in FF,
// the notebook keyboard shortcuts fail.
IPython.keyboard_manager.enable()
\$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items){
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) { continue; };

var button = \$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = \$('<span class="mpl-message" style="text-align:right; float: right;"/>');
nav_element.append(status_bar);
this.message = status_bar[0];

// Add the close button to the window.
var buttongrp = \$('<div class="btn-group inline pull-right"></div>');
var button = \$('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>');
button.click(function (evt) { fig.handle_close(fig, {}); } );
button.mouseover('Stop Interaction', toolbar_mouse_event);
buttongrp.append(button);
var titlebar = this.root.find(\$('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
// select the cell after this one
var index = IPython.notebook.find_cell_index(this.cell_info[0]);
IPython.notebook.select(index + 1);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}

gamma = 0.01  accuracy = 0.91   AUC = 1.00
gamma = 0.10  accuracy = 0.90   AUC = 0.98
gamma = 0.20  accuracy = 0.90   AUC = 0.66
gamma = 1.00  accuracy = 0.90   AUC = 0.50

``````

### Evaluation measures for multi-class classification

#### Multi-class confusion matrix

``````

In [21]:

X, y = dataset.data, dataset.target
X_train_mc, X_test_mc, y_train_mc, y_test_mc = train_test_split(X, y, random_state=0)

svm = SVC(kernel = 'linear').fit(X_train_mc, y_train_mc)
svm_predicted_mc = svm.predict(X_test_mc)
confusion_mc = confusion_matrix(y_test_mc, svm_predicted_mc)
df_cm = pd.DataFrame(confusion_mc,
index = [i for i in range(0,10)], columns = [i for i in range(0,10)])

plt.figure(figsize=(5.5,4))
sns.heatmap(df_cm, annot=True)
plt.title('SVM Linear Kernel \nAccuracy:{0:.3f}'.format(accuracy_score(y_test_mc,
svm_predicted_mc)))
plt.ylabel('True label')
plt.xlabel('Predicted label')

svm = SVC(kernel = 'rbf').fit(X_train_mc, y_train_mc)
svm_predicted_mc = svm.predict(X_test_mc)
confusion_mc = confusion_matrix(y_test_mc, svm_predicted_mc)
df_cm = pd.DataFrame(confusion_mc, index = [i for i in range(0,10)],
columns = [i for i in range(0,10)])

plt.figure(figsize = (5.5,4))
sns.heatmap(df_cm, annot=True)
plt.title('SVM RBF Kernel \nAccuracy:{0:.3f}'.format(accuracy_score(y_test_mc,
svm_predicted_mc)))
plt.ylabel('True label')
plt.xlabel('Predicted label');

``````
``````

var element = \$('#321b1f94-930e-45f4-81b3-e89dfc97e0b4');
/* Put everything inside the global mpl namespace */
window.mpl = {};

mpl.get_websocket_type = function() {
if (typeof(WebSocket) !== 'undefined') {
return WebSocket;
} else if (typeof(MozWebSocket) !== 'undefined') {
return MozWebSocket;
} else {
'Please try Chrome, Safari or Firefox ≥ 6. ' +
'Firefox 4 and 5 are also supported but you ' +
'have to enable WebSockets in about:config.');
};
}

this.id = figure_id;

this.ws = websocket;

this.supports_binary = (this.ws.binaryType != undefined);

if (!this.supports_binary) {
var warnings = document.getElementById("mpl-warnings");
if (warnings) {
warnings.style.display = 'block';
warnings.textContent = (
"This browser does not support binary websocket messages. " +
"Performance may be slow.");
}
}

this.imageObj = new Image();

this.context = undefined;
this.message = undefined;
this.canvas = undefined;
this.rubberband_canvas = undefined;
this.rubberband_context = undefined;
this.format_dropdown = undefined;

this.image_mode = 'full';

this.root = \$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

\$(parent_element).append(this.root);

this._init_canvas(this);
this._init_toolbar(this);

var fig = this;

this.waiting = false;

this.ws.onopen =  function () {
fig.send_message("supports_binary", {value: fig.supports_binary});
fig.send_message("send_image_mode", {});
if (mpl.ratio != 1) {
fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio});
}
fig.send_message("refresh", {});
}

if (fig.image_mode == 'full') {
// Full images could contain transparency (where diff images
// almost always do), so we need to clear the canvas so that
// there is no ghosting.
fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);
}
fig.context.drawImage(fig.imageObj, 0, 0);
};

this.ws.close();
}

this.ws.onmessage = this._make_on_message_function(this);

}

var titlebar = \$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = \$(
'<div class="ui-dialog-title" style="width: 100%; ' +
titlebar.append(titletext)
this.root.append(titlebar);
}

mpl.figure.prototype._canvas_extra_style = function(canvas_div) {

}

mpl.figure.prototype._root_extra_style = function(canvas_div) {

}

mpl.figure.prototype._init_canvas = function() {
var fig = this;

var canvas_div = \$('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = \$('<canvas/>');
canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0")

this.canvas = canvas[0];
this.context = canvas[0].getContext("2d");

var backingStore = this.context.backingStorePixelRatio ||
this.context.webkitBackingStorePixelRatio ||
this.context.mozBackingStorePixelRatio ||
this.context.msBackingStorePixelRatio ||
this.context.oBackingStorePixelRatio ||
this.context.backingStorePixelRatio || 1;

mpl.ratio = (window.devicePixelRatio || 1) / backingStore;

var rubberband = \$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
return false;
});

function set_focus () {
canvas.focus();
canvas_div.focus();
}

window.setTimeout(set_focus, 100);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = \$('<button/>');
button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +
'ui-button-icon-only');
button.attr('role', 'button');
button.attr('aria-disabled', 'false');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);

var icon_img = \$('<span/>');

var tooltip_span = \$('<span/>');
tooltip_span.html(tooltip);

button.append(icon_img);
button.append(tooltip_span);

nav_element.append(button);
}

var fmt_picker_span = \$('<span/>');

var fmt_picker = \$('<select/>');
fmt_picker_span.append(fmt_picker);
nav_element.append(fmt_picker_span);
this.format_dropdown = fmt_picker[0];

for (var ind in mpl.extensions) {
var fmt = mpl.extensions[ind];
var option = \$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}

// Add hover states to the ui-buttons
\$( ".ui-button" ).hover(
function() { \$(this).removeClass("ui-state-hover");}
);

var status_bar = \$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - \$(targ).offset().left;
var y = e.pageY - \$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overriden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = \$("#" + id);

window.open(figure.imageObj.src);
}

var fig = new mpl.figure(id, ws_proxy,
element.get(0));

// Call onopen now - mpl needs it, as it is assuming we've passed it a real
// web socket which is closed, not our websocket->open comm proxy.
ws_proxy.onopen();

fig.parent_element = element.get(0);
fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>");
if (!fig.cell_info) {
console.error("Failed to find cell for figure", id, fig);
return;
}

var output_index = fig.cell_info[2]
var cell = fig.cell_info[0];

};

mpl.figure.prototype.handle_close = function(fig, msg) {
var width = fig.canvas.width/mpl.ratio
fig.root.unbind('remove')

// Update the output cell to use the data from the current canvas.
fig.push_to_output();
var dataURL = fig.canvas.toDataURL();
// Re-enable the keyboard manager in IPython - without this line, in FF,
// the notebook keyboard shortcuts fail.
IPython.keyboard_manager.enable()
\$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items){
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) { continue; };

var button = \$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = \$('<span class="mpl-message" style="text-align:right; float: right;"/>');
nav_element.append(status_bar);
this.message = status_bar[0];

// Add the close button to the window.
var buttongrp = \$('<div class="btn-group inline pull-right"></div>');
var button = \$('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>');
button.click(function (evt) { fig.handle_close(fig, {}); } );
button.mouseover('Stop Interaction', toolbar_mouse_event);
buttongrp.append(button);
var titlebar = this.root.find(\$('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
// select the cell after this one
var index = IPython.notebook.find_cell_index(this.cell_info[0]);
IPython.notebook.select(index + 1);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}

var element = \$('#564955d1-f467-42be-a8b6-a0a52d75bb60');
/* Put everything inside the global mpl namespace */
window.mpl = {};

mpl.get_websocket_type = function() {
if (typeof(WebSocket) !== 'undefined') {
return WebSocket;
} else if (typeof(MozWebSocket) !== 'undefined') {
return MozWebSocket;
} else {
'Please try Chrome, Safari or Firefox ≥ 6. ' +
'Firefox 4 and 5 are also supported but you ' +
'have to enable WebSockets in about:config.');
};
}

this.id = figure_id;

this.ws = websocket;

this.supports_binary = (this.ws.binaryType != undefined);

if (!this.supports_binary) {
var warnings = document.getElementById("mpl-warnings");
if (warnings) {
warnings.style.display = 'block';
warnings.textContent = (
"This browser does not support binary websocket messages. " +
"Performance may be slow.");
}
}

this.imageObj = new Image();

this.context = undefined;
this.message = undefined;
this.canvas = undefined;
this.rubberband_canvas = undefined;
this.rubberband_context = undefined;
this.format_dropdown = undefined;

this.image_mode = 'full';

this.root = \$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

\$(parent_element).append(this.root);

this._init_canvas(this);
this._init_toolbar(this);

var fig = this;

this.waiting = false;

this.ws.onopen =  function () {
fig.send_message("supports_binary", {value: fig.supports_binary});
fig.send_message("send_image_mode", {});
if (mpl.ratio != 1) {
fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio});
}
fig.send_message("refresh", {});
}

if (fig.image_mode == 'full') {
// Full images could contain transparency (where diff images
// almost always do), so we need to clear the canvas so that
// there is no ghosting.
fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);
}
fig.context.drawImage(fig.imageObj, 0, 0);
};

this.ws.close();
}

this.ws.onmessage = this._make_on_message_function(this);

}

var titlebar = \$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = \$(
'<div class="ui-dialog-title" style="width: 100%; ' +
titlebar.append(titletext)
this.root.append(titlebar);
}

mpl.figure.prototype._canvas_extra_style = function(canvas_div) {

}

mpl.figure.prototype._root_extra_style = function(canvas_div) {

}

mpl.figure.prototype._init_canvas = function() {
var fig = this;

var canvas_div = \$('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = \$('<canvas/>');
canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0")

this.canvas = canvas[0];
this.context = canvas[0].getContext("2d");

var backingStore = this.context.backingStorePixelRatio ||
this.context.webkitBackingStorePixelRatio ||
this.context.mozBackingStorePixelRatio ||
this.context.msBackingStorePixelRatio ||
this.context.oBackingStorePixelRatio ||
this.context.backingStorePixelRatio || 1;

mpl.ratio = (window.devicePixelRatio || 1) / backingStore;

var rubberband = \$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
return false;
});

function set_focus () {
canvas.focus();
canvas_div.focus();
}

window.setTimeout(set_focus, 100);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = \$('<button/>');
button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +
'ui-button-icon-only');
button.attr('role', 'button');
button.attr('aria-disabled', 'false');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);

var icon_img = \$('<span/>');

var tooltip_span = \$('<span/>');
tooltip_span.html(tooltip);

button.append(icon_img);
button.append(tooltip_span);

nav_element.append(button);
}

var fmt_picker_span = \$('<span/>');

var fmt_picker = \$('<select/>');
fmt_picker_span.append(fmt_picker);
nav_element.append(fmt_picker_span);
this.format_dropdown = fmt_picker[0];

for (var ind in mpl.extensions) {
var fmt = mpl.extensions[ind];
var option = \$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}

// Add hover states to the ui-buttons
\$( ".ui-button" ).hover(
function() { \$(this).removeClass("ui-state-hover");}
);

var status_bar = \$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - \$(targ).offset().left;
var y = e.pageY - \$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overriden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = \$("#" + id);

window.open(figure.imageObj.src);
}

var fig = new mpl.figure(id, ws_proxy,
element.get(0));

// Call onopen now - mpl needs it, as it is assuming we've passed it a real
// web socket which is closed, not our websocket->open comm proxy.
ws_proxy.onopen();

fig.parent_element = element.get(0);
fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>");
if (!fig.cell_info) {
console.error("Failed to find cell for figure", id, fig);
return;
}

var output_index = fig.cell_info[2]
var cell = fig.cell_info[0];

};

mpl.figure.prototype.handle_close = function(fig, msg) {
var width = fig.canvas.width/mpl.ratio
fig.root.unbind('remove')

// Update the output cell to use the data from the current canvas.
fig.push_to_output();
var dataURL = fig.canvas.toDataURL();
// Re-enable the keyboard manager in IPython - without this line, in FF,
// the notebook keyboard shortcuts fail.
IPython.keyboard_manager.enable()
\$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = \$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items){
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) { continue; };

var button = \$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = \$('<span class="mpl-message" style="text-align:right; float: right;"/>');
nav_element.append(status_bar);
this.message = status_bar[0];

// Add the close button to the window.
var buttongrp = \$('<div class="btn-group inline pull-right"></div>');
var button = \$('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>');
button.click(function (evt) { fig.handle_close(fig, {}); } );
button.mouseover('Stop Interaction', toolbar_mouse_event);
buttongrp.append(button);
var titlebar = this.root.find(\$('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
// select the cell after this one
var index = IPython.notebook.find_cell_index(this.cell_info[0]);
IPython.notebook.select(index + 1);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}

``````

#### Multi-class classification report

``````

In [ ]:

print(classification_report(y_test_mc, svm_predicted_mc))

``````

#### Micro- vs. macro-averaged metrics

``````

In [ ]:

print('Micro-averaged precision = {:.2f} (treat instances equally)'
.format(precision_score(y_test_mc, svm_predicted_mc, average = 'micro')))
print('Macro-averaged precision = {:.2f} (treat classes equally)'
.format(precision_score(y_test_mc, svm_predicted_mc, average = 'macro')))

``````
``````

In [ ]:

print('Micro-averaged f1 = {:.2f} (treat instances equally)'
.format(f1_score(y_test_mc, svm_predicted_mc, average = 'micro')))
print('Macro-averaged f1 = {:.2f} (treat classes equally)'
.format(f1_score(y_test_mc, svm_predicted_mc, average = 'macro')))

``````

### Regression evaluation metrics

``````

In [ ]:

%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn import datasets
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.dummy import DummyRegressor

X = diabetes.data[:, None, 6]
y = diabetes.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

lm = LinearRegression().fit(X_train, y_train)
lm_dummy_mean = DummyRegressor(strategy = 'mean').fit(X_train, y_train)

y_predict = lm.predict(X_test)
y_predict_dummy_mean = lm_dummy_mean.predict(X_test)

print('Linear model, coefficients: ', lm.coef_)
print("Mean squared error (dummy): {:.2f}".format(mean_squared_error(y_test,
y_predict_dummy_mean)))
print("Mean squared error (linear model): {:.2f}".format(mean_squared_error(y_test, y_predict)))
print("r2_score (dummy): {:.2f}".format(r2_score(y_test, y_predict_dummy_mean)))
print("r2_score (linear model): {:.2f}".format(r2_score(y_test, y_predict)))

# Plot outputs
plt.scatter(X_test, y_test,  color='black')
plt.plot(X_test, y_predict, color='green', linewidth=2)
plt.plot(X_test, y_predict_dummy_mean, color='red', linestyle = 'dashed',
linewidth=2, label = 'dummy')

plt.show()

``````

### Model selection using evaluation metrics

#### Cross-validation example

``````

In [ ]:

from sklearn.model_selection import cross_val_score
from sklearn.svm import SVC

# again, making this a binary problem with 'digit 1' as positive class
# and 'not 1' as negative class
X, y = dataset.data, dataset.target == 1
clf = SVC(kernel='linear', C=1)

# accuracy is the default scoring metric
print('Cross-validation (accuracy)', cross_val_score(clf, X, y, cv=5))
# use AUC as scoring metric
print('Cross-validation (AUC)', cross_val_score(clf, X, y, cv=5, scoring = 'roc_auc'))
# use recall as scoring metric
print('Cross-validation (recall)', cross_val_score(clf, X, y, cv=5, scoring = 'recall'))

``````

#### Grid search example

``````

In [ ]:

from sklearn.svm import SVC
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import roc_auc_score

X, y = dataset.data, dataset.target == 1
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

clf = SVC(kernel='rbf')
grid_values = {'gamma': [0.001, 0.01, 0.05, 0.1, 1, 10, 100]}

# default metric to optimize over grid parameters: accuracy
grid_clf_acc = GridSearchCV(clf, param_grid = grid_values)
grid_clf_acc.fit(X_train, y_train)
y_decision_fn_scores_acc = grid_clf_acc.decision_function(X_test)

print('Grid best parameter (max. accuracy): ', grid_clf_acc.best_params_)
print('Grid best score (accuracy): ', grid_clf_acc.best_score_)

# alternative metric to optimize over grid parameters: AUC
grid_clf_auc = GridSearchCV(clf, param_grid = grid_values, scoring = 'roc_auc')
grid_clf_auc.fit(X_train, y_train)
y_decision_fn_scores_auc = grid_clf_auc.decision_function(X_test)

print('Test set AUC: ', roc_auc_score(y_test, y_decision_fn_scores_auc))
print('Grid best parameter (max. AUC): ', grid_clf_auc.best_params_)
print('Grid best score (AUC): ', grid_clf_auc.best_score_)

``````

#### Evaluation metrics supported for model selection

``````

In [ ]:

from sklearn.metrics.scorer import SCORERS

print(sorted(list(SCORERS.keys())))

``````

### Two-feature classification example using the digits dataset

#### Optimizing a classifier using different evaluation metrics

``````

In [ ]:

from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.model_selection import GridSearchCV

X, y = dataset.data, dataset.target == 1
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

# Create a two-feature input vector matching the example plot above
# We jitter the points (add a small amount of random noise) in case there are areas
# in feature space where many instances have the same features.
jitter_delta = 0.25
X_twovar_train = X_train[:,[20,59]]+ np.random.rand(X_train.shape[0], 2) - jitter_delta
X_twovar_test  = X_test[:,[20,59]] + np.random.rand(X_test.shape[0], 2) - jitter_delta

clf = SVC(kernel = 'linear').fit(X_twovar_train, y_train)
grid_values = {'class_weight':['balanced', {1:2},{1:3},{1:4},{1:5},{1:10},{1:20},{1:50}]}
plt.figure(figsize=(9,6))
for i, eval_metric in enumerate(('precision','recall', 'f1','roc_auc')):
grid_clf_custom = GridSearchCV(clf, param_grid=grid_values, scoring=eval_metric)
grid_clf_custom.fit(X_twovar_train, y_train)
print('Grid best parameter (max. {0}): {1}'
.format(eval_metric, grid_clf_custom.best_params_))
print('Grid best score ({0}): {1}'
.format(eval_metric, grid_clf_custom.best_score_))
plot_class_regions_for_classifier_subplot(grid_clf_custom, X_twovar_test, y_test, None,
None, None,  plt.subplot(2, 2, i+1))

plt.title(eval_metric+'-oriented SVC')
plt.tight_layout()
plt.show()

``````

#### Precision-recall curve for the default SVC classifier (with balanced class weights)

``````

In [ ]:

from sklearn.model_selection import train_test_split
from sklearn.metrics import precision_recall_curve
from sklearn.svm import SVC

X, y = dataset.data, dataset.target == 1
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

# create a two-feature input vector matching the example plot above
jitter_delta = 0.25
X_twovar_train = X_train[:,[20,59]]+ np.random.rand(X_train.shape[0], 2) - jitter_delta
X_twovar_test  = X_test[:,[20,59]] + np.random.rand(X_test.shape[0], 2) - jitter_delta

clf = SVC(kernel='linear', class_weight='balanced').fit(X_twovar_train, y_train)

y_scores = clf.decision_function(X_twovar_test)

precision, recall, thresholds = precision_recall_curve(y_test, y_scores)
closest_zero = np.argmin(np.abs(thresholds))
closest_zero_p = precision[closest_zero]
closest_zero_r = recall[closest_zero]

plot_class_regions_for_classifier(clf, X_twovar_test, y_test)
plt.title("SVC, class_weight = 'balanced', optimized for accuracy")
plt.show()

plt.figure()
plt.xlim([0.0, 1.01])
plt.ylim([0.0, 1.01])
plt.title ("Precision-recall curve: SVC, class_weight = 'balanced'")
plt.plot(precision, recall, label = 'Precision-Recall Curve')
plt.plot(closest_zero_p, closest_zero_r, 'o', markersize=12, fillstyle='none', c='r', mew=3)
plt.xlabel('Precision', fontsize=16)
plt.ylabel('Recall', fontsize=16)
plt.axes().set_aspect('equal')
plt.show()
print('At zero threshold, precision: {:.2f}, recall: {:.2f}'
.format(closest_zero_p, closest_zero_r))

``````
``````

In [ ]:

``````