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Support Vector Machine

A common task in Machine Learning is to classify data. Given a data point cloud, sometimes linear classification is impossible. In those cases we can use a Support Vector Machine instead, but an SVM can also work with linear separation.

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Dataset
We loading the Iris data, which we’ll later use to classify. This set has many features, but we’ll use only the first two features:

  • sepal length
  • sepal width
The code below will load the data points on the decision surface.


import matplotlib
matplotlib.use('GTKAgg')

import numpy as np
import matplotlib.pyplot as plt
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

# create a mesh to plot in
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))

# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.coolwarm)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.title('Data')
plt.show()

svm data

Support Vector Machine Example
Separating two point clouds is easy with a linear line, but what if they cannot be separated by a linear line?

In that case we can use a kernel, a kernel is a function that a domain-expert provides to a machine learning algorithm (a kernel is not limited to an svm).

The example below shows SVM decision surface using 4 different kernels, of which two are linear kernels.


import matplotlib
matplotlib.use('GTKAgg')

import numpy as np
import matplotlib.pyplot as plt
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. We could
# avoid this ugly slicing by using a two-dim dataset
y = iris.target

h = .02 # step size in the mesh

# we create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
C = 1.0 # SVM regularization parameter
svc = svm.SVC(kernel='linear', C=C).fit(X, y)
rbf_svc = svm.SVC(kernel='rbf', gamma=0.7, C=C).fit(X, y)
poly_svc = svm.SVC(kernel='poly', degree=3, C=C).fit(X, y)
lin_svc = svm.LinearSVC(C=C).fit(X, y)

# create a mesh to plot in
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))

# title for the plots
titles = ['SVC with linear kernel',
'LinearSVC (linear kernel)',
'SVC with RBF kernel',
'SVC with polynomial (degree 3) kernel']

for i, clf in enumerate((svc, lin_svc, rbf_svc, poly_svc)):
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
plt.subplot(2, 2, i + 1)
plt.subplots_adjust(wspace=0.4, hspace=0.4)

Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])

# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)

# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.coolwarm)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.title(titles[i])

plt.show()

svm-classify

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