In [1]:
import numpy as np
import pylab as pl
from sklearn import svm
# we create 40 separable points
np.random.seed(0)
X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]
Y = [0] * 20 + [1] * 20
# fit the model
clf = svm.SVC(kernel='linear')
clf.fit(X, Y)
# get the separating hyperplane
w = clf.coef_[0]
a = -w[0] / w[1]
xx = np.linspace(-5, 5)
yy = a * xx - (clf.intercept_[0]) / w[1]
# plot the parallels to the separating hyperplane that pass through the
# support vectors
b = clf.support_vectors_[0]
yy_down = a * xx + (b[1] - a * b[0])
b = clf.support_vectors_[-1]
yy_up = a * xx + (b[1] - a * b[0])
# plot the line, the points, and the nearest vectors to the plane
pl.plot(xx, yy, 'k-')
pl.plot(xx, yy_down, 'k--')
pl.plot(xx, yy_up, 'k--')
pl.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
s=80, facecolors='none')
pl.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired)
pl.axis('tight')
pl.show()
In [1]:
In [2]:
import numpy as np
import pylab as pl
from sklearn import svm, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features.
Y = iris.target
h = .02 # step size in the mesh
clf = svm.SVC(C=1.0, kernel='linear')
# we create an instance of SVM Classifier and fit the data.
clf.fit(X, Y)
# Plot the decision boundary. For that, we will asign 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, h), np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
pl.figure(1, figsize=(4, 3))
pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
# Plot also the training points
pl.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired)
pl.xlabel('Sepal length')
pl.ylabel('Sepal width')
pl.xlim(xx.min(), xx.max())
pl.ylim(yy.min(), yy.max())
pl.xticks(())
pl.yticks(())
pl.show()
In [2]:
In [3]:
import numpy as np
import pylab as pl
from sklearn import svm
# Our dataset and targets
X = np.c_[(.4, -.7),
(-1.5, -1),
(-1.4, -.9),
(-1.3, -1.2),
(-1.1, -.2),
(-1.2, -.4),
(-.5, 1.2),
(-1.5, 2.1),
(1, 1),
# --
(1.3, .8),
(1.2, .5),
(.2, -2),
(.5, -2.4),
(.2, -2.3),
(0, -2.7),
(1.3, 2.1),
].T
Y = [0] * 8 + [1] * 8
# figure number
fignum = 1
# fit the model
for kernel in ('linear', 'poly', 'rbf'):
clf = svm.SVC(kernel=kernel, gamma=2)
clf.fit(X, Y)
# plot the line, the points, and the nearest vectors to the plane
pl.figure(fignum, figsize=(4, 3))
pl.clf()
pl.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
s=80, facecolors='none', zorder=10)
pl.scatter(X[:, 0], X[:, 1], c=Y, zorder=10, cmap=pl.cm.Paired)
pl.axis('tight')
x_min = -3
x_max = 3
y_min = -3
y_max = 3
XX, YY = np.mgrid[x_min:x_max:200j, y_min:y_max:200j]
Z = clf.decision_function(np.c_[XX.ravel(), YY.ravel()])
# Put the result into a color plot
Z = Z.reshape(XX.shape)
pl.figure(fignum, figsize=(4, 3))
pl.pcolormesh(XX, YY, Z > 0, cmap=pl.cm.Paired)
pl.contour(XX, YY, Z, colors=['k', 'k', 'k'],
linestyles=['--', '-', '--'],
levels=[-.5, 0, .5])
pl.xlim(x_min, x_max)
pl.ylim(y_min, y_max)
pl.xticks(())
pl.yticks(())
fignum = fignum + 1
pl.show()
In [3]:
In [4]:
import numpy as np
import pylab as pl
from sklearn.svm import SVC
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_iris
from sklearn.cross_validation import StratifiedKFold
from sklearn.grid_search import GridSearchCV
##############################################################################
# Load and prepare data set
#
# dataset for grid search
iris = load_iris()
X = iris.data
Y = iris.target
# dataset for decision function visualization
X_2d = X[:, :2]
X_2d = X_2d[Y > 0]
Y_2d = Y[Y > 0]
Y_2d -= 1
# It is usually a good idea to scale the data for SVM training.
# We are cheating a bit in this example in scaling all of the data,
# instead of fitting the transformation on the training set and
# just applying it on the test set.
scaler = StandardScaler()
X = scaler.fit_transform(X)
X_2d = scaler.fit_transform(X_2d)
##############################################################################
# Train classifier
#
# For an initial search, a logarithmic grid with basis
# 10 is often helpful. Using a basis of 2, a finer
# tuning can be achieved but at a much higher cost.
C_range = 10.0 ** np.arange(-2, 9)
gamma_range = 10.0 ** np.arange(-5, 4)
param_grid = dict(gamma=gamma_range, C=C_range)
cv = StratifiedKFold(y=Y, n_folds=3)
grid = GridSearchCV(SVC(), param_grid=param_grid, cv=cv)
grid.fit(X, Y)
print("The best classifier is: ", grid.best_estimator_)
# Now we need to fit a classifier for all parameters in the 2d version
# (we use a smaller set of parameters here because it takes a while to train)
C_2d_range = [1, 1e2, 1e4]
gamma_2d_range = [1e-1, 1, 1e1]
classifiers = []
for C in C_2d_range:
for gamma in gamma_2d_range:
clf = SVC(C=C, gamma=gamma)
clf.fit(X_2d, Y_2d)
classifiers.append((C, gamma, clf))
##############################################################################
# visualization
#
# draw visualization of parameter effects
pl.figure(figsize=(8, 6))
xx, yy = np.meshgrid(np.linspace(-5, 5, 200), np.linspace(-5, 5, 200))
for (k, (C, gamma, clf)) in enumerate(classifiers):
# evaluate decision function in a grid
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
# visualize decision function for these parameters
pl.subplot(len(C_2d_range), len(gamma_2d_range), k + 1)
pl.title("gamma 10^%d, C 10^%d" % (np.log10(gamma), np.log10(C)),
size='medium')
# visualize parameter's effect on decision function
pl.pcolormesh(xx, yy, -Z, cmap=pl.cm.jet)
pl.scatter(X_2d[:, 0], X_2d[:, 1], c=Y_2d, cmap=pl.cm.jet)
pl.xticks(())
pl.yticks(())
pl.axis('tight')
# plot the scores of the grid
# grid_scores_ contains parameter settings and scores
score_dict = grid.grid_scores_
# We extract just the scores
scores = [x[1] for x in score_dict]
scores = np.array(scores).reshape(len(C_range), len(gamma_range))
# draw heatmap of accuracy as a function of gamma and C
pl.figure(figsize=(8, 6))
pl.subplots_adjust(left=0.05, right=0.95, bottom=0.15, top=0.95)
pl.imshow(scores, interpolation='nearest', cmap=pl.cm.spectral)
pl.xlabel('gamma')
pl.ylabel('C')
pl.colorbar()
pl.xticks(np.arange(len(gamma_range)), gamma_range, rotation=45)
pl.yticks(np.arange(len(C_range)), C_range)
pl.show()
In [6]:
"""
================================
Nearest Neighbors Classification
================================
Sample usage of Nearest Neighbors classification.
It will plot the decision boundaries for each class.
"""
print __doc__
import numpy as np
import pylab as pl
from matplotlib.colors import ListedColormap
from sklearn import neighbors, datasets
n_neighbors = 15
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
y = iris.target
h = .02 # step size in the mesh
# Create color maps
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
for weights in ['uniform', 'distance']:
# we create an instance of Neighbours Classifier and fit the data.
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# Plot the decision boundary. For that, we will asign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
pl.figure()
pl.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
pl.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
pl.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
pl.axis('tight')
pl.show()
In [ ]: