I have found this really cool notebook on SVM :
https://github.com/jakevdp/sklearn_tutorial/blob/master/notebooks/03.1-Classification-SVMs.ipynb
But was a bit frustrated 'cause it doesn't show how to plot the maximum-margin in 3-space. I've tried my best but have no clue about how to do it... For instance I'd like to plot it on the following reprsentation (which is taken from the notebook):
Also, if suport vectors could be encircled it would be the sherry on the top.
This is a very good question, however the notebook provided is actually "lying". This not how kernel works, and while this visualization is cool, it is not what happens "inside SVM". Lets put this aside though and focus on how to plot 3D separation hyperplane in this projected space (which is not RBF projected space).
All you have to do is:
clf.coefs_ and one for clf.intercept_, when I need to input 3 for normal (a,b,c) and 3 for point (x,y,z), according to the link you posted.
clf.coefs_ provides 3 values and not 2. Thanks to your help I managed to plot the hyperplane.
import numpy as np
from sklearn.svm import SVC
from sklearn.datasets import make_circles
X_1_2, y = make_circles(100, factor = .1, noise=.1)
X_3 = np.exp(-(X_1_2[:,0] ** 2 + X_1_2[:,1] ** 2))
X = np.insert(X_1_2, 2, X_3, axis=1)
clf = SVC(kernel='linear').fit(X,y)
w = clf.coef_
w1 = w [:, 0]
w2 = w [:, 1]
w3 = w [:, 2]
b = clf.intercept_
sv = clf.support_vectors_
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
xx, yy = np.meshgrid(range(-1,2), range(-1,2))
zz = (-w1 * xx - w2 * yy - b) * 1. /w3
%matplotlib notebook
plt3d = plt.subplot(projection='3d')
plt3d.plot_wireframe(xx, yy, zz, rstride=1, cstride=1, color='purple')
plt3d.scatter3D(X[:, 0], X[:, 1], X[:, 2], c=y, s=50, cmap='winter')
plt3d.scatter3D(sv[:, 0], sv[:, 1], sv[:, 2], s=150)
plt.show()
