Extract decision boundary with scikit-learn linear SVM

Question

I have a very simple 1D classification problem: a list of values [0, 0.5, 2] and their associated classes [0, 1, 2]. I would like to get the classification boundaries between th

Answer 1

Get decision line from SVM, demo 1

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm
from sklearn.datasets import make_blobs
# we create 40 separable points
X, y = make_blobs(n_samples=40, centers=2, random_state=6)
# fit the model, don't regularize for illustration purposes
clf = svm.SVC(kernel='linear', C=1000)
clf.fit(X, y)
plt.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.Paired)
# plot the decision function
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
# create grid to evaluate model
xx = np.linspace(xlim[0], xlim[1], 30)
yy = np.linspace(ylim[0], ylim[1], 30)
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T
Z = clf.decision_function(xy).reshape(XX.shape)
# plot decision boundary and margins
ax.contour(XX, YY, Z, colors='k', levels=[-1, 0, 1], alpha=0.5,
           linestyles=['--', '-', '--'])
# plot support vectors
ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=100,
           linewidth=1, facecolors='none')
plt.show()

Prints:

Approximate the separating n-1 dimensional hyperplane of an SVM, Demo 2

import numpy as np
import mlpy
from sklearn import svm
from sklearn.svm import SVC
import matplotlib.pyplot as plt
np.random.seed(0)
mean1, cov1, n1 = [1, 5], [[1,1],[1,2]], 200  # 200 samples of class 1
x1 = np.random.multivariate_normal(mean1, cov1, n1)
y1 = np.ones(n1, dtype=np.int)

mean2, cov2, n2 = [2.5, 2.5], [[1,0],[0,1]], 300 # 300 samples of class -1
x2 = np.random.multivariate_normal(mean2, cov2, n2)
y2 = 0 * np.ones(n2, dtype=np.int)
X = np.concatenate((x1, x2), axis=0) # concatenate the 1 and -1 samples
y = np.concatenate((y1, y2))
clf = svm.SVC()
#fit the hyperplane between the clouds of data, should be fast as hell
clf.fit(X, y)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, 
    decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
    max_iter=-1, probability=False, random_state=None, shrinking=True,
    tol=0.001, verbose=False)

production_point = [1., 2.5]

answer = clf.predict([production_point])
print("Answer: " + str(answer))
plt.plot(x1[:,0], x1[:,1], 'ob', x2[:,0], x2[:,1], 'or', markersize = 5)
colormap = ['r', 'b']
color = colormap[answer[0]]
plt.plot(production_point[0], production_point[1], 'o' + str(color), markersize=20)

#I want to draw the decision lines
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
xx = np.linspace(xlim[0], xlim[1], 30)
yy = np.linspace(ylim[0], ylim[1], 30)
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T
Z = clf.decision_function(xy).reshape(XX.shape)
ax.contour(XX, YY, Z, colors='k', levels=[-1, 0, 1], alpha=0.5,
           linestyles=['--', '-', '--'])
plt.show()

Prints:

These hyperplanes are all straight as an arrow, they're just straight in higher dimensions and can't be comprehended by mere mortals confined to 3 dimensional space. These hyperplanes are cast into higher dimensions with the creative kernel functions, than flattened back into the visible dimension for your viewing pleasure. Here is a video trying to impart some intuition of what is going on in demo 2: https://www.youtube.com/watch?v=3liCbRZPrZA