Plot maximum-margin hyperplane in 3-space with Python

Question

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.

score 2 · Accepted Answer · edited May 23 '17 at 12:24

2

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:

Fit linear SVM to the 3D data used for this plot.
Extract weights (clf.coefs_) and bias (clf.intercept_)
Plot 3d hyperplane with normal (clf.coefs_) and distance from the origin (clf.intercept_)

edited May 23 '17 at 12:24

Community

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answered Dec 21 '16 at 17:42

lejlot

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Thx a lot lejlot, I'm stuck at step 3 though. I have 2 values for `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. – crocefisso Dec 23 '16 at 09:23
you have to fit on 3d data you plotted, which, in your case is x, y, k(x, y), thus you will have **three** coefs – lejlot Dec 23 '16 at 12:04
You're completely right thx, `clf.coefs_` provides 3 values and not 2. Thanks to your help I managed to [plot the hyperplane](https://s23.postimg.org/w1bzmkg7v/index.png). – crocefisso Dec 25 '16 at 20:09
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[Here](http://www.novagen.tech/wp-content/uploads/2017/01/JupyterVSZeppelin.pdf) you can find my code. – crocefisso Jan 09 '17 at 13:38

crocefisso · Answer 2 · 2021-01-05T14:48:54.477

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()

Plot maximum-margin hyperplane in 3-space with Python

2 Answers2