/scikit-learn

# Plot different SVM classifiers in the iris dataset

Comparison of different linear SVM classifiers on a 2D projection of the iris dataset. We only consider the first 2 features of this dataset:

• Sepal length
• Sepal width

This example shows how to plot the decision surface for four SVM classifiers with different kernels.

The linear models `LinearSVC()` and `SVC(kernel='linear')` yield slightly different decision boundaries. This can be a consequence of the following differences:

• `LinearSVC` minimizes the squared hinge loss while `SVC` minimizes the regular hinge loss.
• `LinearSVC` uses the One-vs-All (also known as One-vs-Rest) multiclass reduction while `SVC` uses the One-vs-One multiclass reduction.

Both linear models have linear decision boundaries (intersecting hyperplanes) while the non-linear kernel models (polynomial or Gaussian RBF) have more flexible non-linear decision boundaries with shapes that depend on the kind of kernel and its parameters.

Note

while plotting the decision function of classifiers for toy 2D datasets can help get an intuitive understanding of their respective expressive power, be aware that those intuitions don’t always generalize to more realistic high-dimensional problems.

```print(__doc__)

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets

def make_meshgrid(x, y, h=.02):
"""Create a mesh of points to plot in

Parameters
----------
x: data to base x-axis meshgrid on
y: data to base y-axis meshgrid on
h: stepsize for meshgrid, optional

Returns
-------
xx, yy : ndarray
"""
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
return xx, yy

def plot_contours(ax, clf, xx, yy, **params):
"""Plot the decision boundaries for a classifier.

Parameters
----------
ax: matplotlib axes object
clf: a classifier
xx: meshgrid ndarray
yy: meshgrid ndarray
params: dictionary of params to pass to contourf, optional
"""
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out

# import some data to play with
# Take the first two features. We could avoid this by using a two-dim dataset
X = iris.data[:, :2]
y = iris.target

# 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
models = (svm.SVC(kernel='linear', C=C),
svm.LinearSVC(C=C),
svm.SVC(kernel='rbf', gamma=0.7, C=C),
svm.SVC(kernel='poly', degree=3, C=C))
models = (clf.fit(X, y) for clf in models)

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

# Set-up 2x2 grid for plotting.
fig, sub = plt.subplots(2, 2)

X0, X1 = X[:, 0], X[:, 1]
xx, yy = make_meshgrid(X0, X1)

for clf, title, ax in zip(models, titles, sub.flatten()):
plot_contours(ax, clf, xx, yy,
cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xlabel('Sepal length')
ax.set_ylabel('Sepal width')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)

plt.show()
```

Total running time of the script: ( 0 minutes 0.487 seconds)

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