by Alejandro Correa Bahnsen and Jesus Solano
version 1.3, January 2019
This notebook is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. Special thanks goes to Rick Muller, Sandia National Laboratories
In this section we will begin to explore the basic principles of machine learning. Machine Learning is about building programs with tunable parameters (typically an array of floating point values) that are adjusted automatically so as to improve their behavior by adapting to previously seen data.
Machine Learning can be considered a subfield of Artificial Intelligence since those algorithms can be seen as building blocks to make computers learn to behave more intelligently by somehow generalizing rather that just storing and retrieving data items like a database system would do.
We'll take a look at two very simple machine learning tasks here. The first is a classification task: the figure shows a collection of two-dimensional data, colored according to two different class labels.
In [1]:
# Import libraries
%matplotlib inline
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns
sns.set();
cmap = mpl.colors.ListedColormap(sns.color_palette("hls", 3))
In [2]:
# Create a random set of examples
from sklearn.datasets.samples_generator import make_blobs
X, Y = make_blobs(n_samples=50, centers=2,random_state=23, cluster_std=2.90)
plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=cmap)
plt.show()
A classification algorithm may be used to draw a dividing boundary between the two clusters of points:
In [4]:
from sklearn.linear_model import SGDClassifier
clf = SGDClassifier(loss="hinge", alpha=0.01, max_iter=300, tol= 0.001, fit_intercept=True)
clf.fit(X, Y)
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In [5]:
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, .05), np.arange(y_min, y_max, .05))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)
In [6]:
plt.contour(xx, yy, Z)
plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=cmap)
plt.show()
This may seem like a trivial task, but it is a simple version of a very important concept. By drawing this separating line, we have learned a model which can generalize to new data: if you were to drop another point onto the plane which is unlabeled, this algorithm could now predict whether it's a blue or a red point.
The next simple task we'll look at is a regression task: a simple best-fit line to a set of data:
In [7]:
a = 0.5
b = 1.0
# x from 0 to 10
x = 30 * np.random.random(20)
# y = a*x + b with noise
y = a * x + b + np.random.normal(size=x.shape)
plt.scatter(x, y)
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In [8]:
from sklearn.linear_model import LinearRegression
clf = LinearRegression()
clf.fit(x[:, None], y)
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In [9]:
# underscore at the end indicates a fit parameter
print(clf.coef_)
print(clf.intercept_)
In [15]:
x_new = np.linspace(0, 30, 100)
y_new = clf.predict(x_new[:, None])
plt.scatter(x, y)
plt.plot(x_new, y_new, 'g-')
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Again, this is an example of fitting a model to data, such that the model can make generalizations about new data. The model has been learned from the training data, and can be used to predict the result of test data: here, we might be given an x-value, and the model would allow us to predict the y value. Again, this might seem like a trivial problem, but it is a basic example of a type of operation that is fundamental to machine learning tasks.
Machine learning is about creating models from data: for that reason, we'll start by discussing how data can be represented in order to be understood by the computer. Along with this, we'll build on our matplotlib examples from the previous section and show some examples of how to visualize data.
Most machine learning algorithms implemented in scikit-learn expect data to be stored in a
two-dimensional array or matrix. The arrays can be
either numpy arrays, or in some cases scipy.sparse matrices.
The size of the array is expected to be [n_samples, n_features]
The number of features must be fixed in advance. However it can be very high dimensional
(e.g. millions of features) with most of them being zeros for a given sample. This is a case
where scipy.sparse matrices can be useful, in that they are
much more memory-efficient than numpy arrays.
In [16]:
from IPython.core.display import Image, display
imp_path = 'https://raw.githubusercontent.com/jakevdp/sklearn_pycon2015/master/notebooks/images/'
display(Image(url=imp_path+'iris_setosa.jpg'))
print("Iris Setosa\n")
display(Image(url=imp_path+'iris_versicolor.jpg'))
print("Iris Versicolor\n")
display(Image(url=imp_path+'iris_virginica.jpg'))
print("Iris Virginica")
display(Image(url='https://raw.githubusercontent.com/albahnsen/PracticalMachineLearningClass/6160065e1e574a20edddc47116a0512d20656e26/notebooks/iris_with_length.png'))
print('Iris versicolor and the petal and sepal width and length')
print('From, Python Data Analytics, Apress, 2015.')
If we want to design an algorithm to recognize iris species, what might the data be?
Remember: we need a 2D array of size [n_samples x n_features].
What would the n_samples refer to?
What might the n_features refer to?
Remember that there must be a fixed number of features for each sample, and feature
number i must be a similar kind of quantity for each sample.
Scikit-learn has a very straightforward set of data on these iris species. The data consist of the following:
Features in the Iris dataset:
Target classes to predict:
scikit-learn embeds a copy of the iris CSV file along with a helper function to load it into numpy arrays:
In [18]:
from sklearn.datasets import load_iris
iris = load_iris()
iris.keys()
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In [19]:
n_samples, n_features = iris.data.shape
print((n_samples, n_features))
print(iris.data[0])
In [20]:
print(iris.data.shape)
print(iris.target.shape)
In [21]:
print(iris.target)
print(iris.target_names)
This data is four dimensional, but we can visualize two of the dimensions at a time using a simple scatter-plot:
In [22]:
import pandas as pd # Pandas is a topic of next session
data_temp = pd.DataFrame(iris.data, columns=iris.feature_names)
data_temp['target'] = iris.target
data_temp['target'] = data_temp['target'].astype('category')
data_temp['target'].cat.categories = iris.target_names
sns.pairplot(data_temp, hue='target', palette=sns.color_palette("hls", 3))
Out[22]:
Principal Component Analysis (PCA) is a dimension reduction technique that can find the combinations of variables that explain the most variance.
Consider the iris dataset. It cannot be visualized in a single 2D plot, as it has 4 features. We are going to extract 2 combinations of sepal and petal dimensions to visualize it:
In [23]:
X, y = iris.data, iris.target
from sklearn.decomposition import PCA
pca = PCA(n_components=3)
pca.fit(X)
X_reduced = pca.transform(X)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)
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In [24]:
X, y = iris.data, iris.target
from sklearn.manifold import Isomap
pca = Isomap(n_components=3)
pca.fit(X)
X_reduced = pca.transform(X)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)
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In [25]:
X_reduced.shape
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In [26]:
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)
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In [27]:
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = Axes3D(fig)
ax.set_title('Iris Dataset by PCA', size=14)
ax.scatter(X_reduced[:,0],X_reduced[:,1],X_reduced[:,2], c=y, cmap=cmap)
ax.set_xlabel('First eigenvector')
ax.set_ylabel('Second eigenvector')
ax.set_zlabel('Third eigenvector')
ax.w_xaxis.set_ticklabels(())
ax.w_yaxis.set_ticklabels(())
ax.w_zaxis.set_ticklabels(())
plt.show()
In [28]:
from sklearn.cluster import KMeans
k_means = KMeans(n_clusters=3, random_state=0) # Fixing the RNG in kmeans
k_means.fit(X)
y_pred = k_means.predict(X)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y_pred, cmap=cmap);
Lets then evaluate the performance of the clustering versus the ground truth
In [29]:
from sklearn.metrics import confusion_matrix
# Compute confusion matrix
cm = confusion_matrix(y, y_pred)
np.set_printoptions(precision=2)
print(cm)
In [30]:
def plot_confusion_matrix(cm, title='Confusion matrix', cmap=plt.cm.Blues):
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(iris.target_names))
plt.xticks(tick_marks, iris.target_names, rotation=45)
plt.yticks(tick_marks, iris.target_names)
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
In [31]:
plt.figure()
plot_confusion_matrix(cm)
In [48]:
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
errors = []
for i in range(1000):
X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.4, random_state=i)
clf = LogisticRegression(multi_class='multinomial',solver='lbfgs',max_iter=1000)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
acc = (y_pred == y_test).sum()
err = 1- acc / n_samples
errors.append(err)
plt.plot(list(range(1000)), errors)
errors = np.array(errors)
print(errors.max(), errors.min(), errors.mean(), errors.std())
In [50]:
from sklearn.ensemble import RandomForestClassifier
errors = []
for i in range(1000):
X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.4, random_state=i)
clf = RandomForestClassifier(n_estimators=10)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
acc = (y_pred == y_test).sum()
err = 1- acc / n_samples
errors.append(err)
plt.plot(list(range(1000)), errors)
errors = np.array(errors)
print(errors.max(), errors.min(), errors.mean(), errors.std())
Scikit-learn strives to have a uniform interface across all methods,
and we'll see examples of these below. Given a scikit-learn estimator
object named model, the following methods are available:
model.fit() : fit training data. For supervised learning applications,
this accepts two arguments: the data X and the labels y (e.g. model.fit(X, y)).
For unsupervised learning applications, this accepts only a single argument,
the data X (e.g. model.fit(X)).model.predict() : given a trained model, predict the label of a new set of data.
This method accepts one argument, the new data X_new (e.g. model.predict(X_new)),
and returns the learned label for each object in the array.model.predict_proba() : For classification problems, some estimators also provide
this method, which returns the probability that a new observation has each categorical label.
In this case, the label with the highest probability is returned by model.predict().model.score() : for classification or regression problems, most (all?) estimators implement
a score method. Scores are between 0 and 1, with a larger score indicating a better fit.model.predict() : predict labels in clustering algorithms.model.transform() : given an unsupervised model, transform new data into the new basis.
This also accepts one argument X_new, and returns the new representation of the data based
on the unsupervised model.model.fit_transform() : some estimators implement this method,
which more efficiently performs a fit and a transform on the same input data.This is a flow chart created by scikit-learn super-contributor Andreas Mueller which gives a nice summary of which algorithms to choose in various situations. Keep it around as a handy reference!
In [29]:
from IPython.display import Image
Image(url="http://scikit-learn.org/dev/_static/ml_map.png")
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Original source on the scikit-learn website