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My first question so please bear with me :)

I use the Shogun toolbox to work with SVM in Python. I just experiment first to get a better understanding of SVM's. I wrote something in Python with some data points to linearly separate. I use the LibSVM()

X = np.array([[2.0,  2.0, 1.0, 1.0],               
              [1.0, -1.0, 1.0, -1.0]])

Y = np.array([[4.0, 5.0,  5.0, 4.0],
              [1.0, 1.0, -1.0, -1.0]])

sample data points

After training the SVM with the given data I can retrieve its bias(get_bias()), the support vectors(get_support_vectors()) and other properties. What I can't get done is plotting the line/hyperplane. I know the equation for the hyperplane is y=wx + b but how to write/plot this down to see it in my figure.

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2 Answers 2

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for a complete example

enter image description here

import numpy as np
import matplotlib.pyplot as plt

def __intersect(rect, line):
    l = []
    xmin,xmax,ymin,ymax = rect
    a,b,c = line

    assert a!=0 or b!=0

    if a == 0:
        y = -c/b
        if y<=ymax and y>=ymin:
            l.append((xmin, y))
            l.append((xmax, y))
        return l
    if b == 0:
        x = -c/a
        if x<=xmax and x>=xmin:
            l.append((x, ymin))
            l.append((x, ymax))
        return l

    k = -a/b
    m = -c/b
    for x in (xmin, xmax):
        y = k*x+m
        if y<=ymax and y>= ymin:
            l.append((x,y))

    k = -b/a
    m = -c/a
    for y in (ymin, ymax):
        x = k*y+m
        if x<xmax and x> xmin:
            l.append((x,y))
    return l


def plotline(coef, *args, **kwargs):
    '''plot line: y=a*x+b or a*x+b*y+c=0'''
    coef = np.float64(coef[:])
    assert len(coef)==2 or len(coef)==3
    if len(coef) == 2:
        a, b, c = coef[0], -1., coef[1]
    elif len(coef) == 3:
        a, b, c = coef
    ax = plt.gca()

    limits = ax.axis()
    points = __intersect(limits, (a,b,c))
    if len(points) == 2:
        pts = np.array(points)
        ax.plot(pts[:,0], pts[:,1], *args, **kwargs)
        ax.axis(limits)

def circle_out(x, y, s=20, *args, **kwargs):
    '''Circle out points with size 's' and edgecolors'''
    ax = plt.gca()
    if 'edgecolors' not in kwargs:
        kwargs['edgecolors'] = 'g'
    ax.scatter(x, y, s, facecolors='none', *args, **kwargs)


def plotSVM(coef, support_vectors=None):
    coef1 = coef[:]
    coef2 = coef[:]
    coef1[2] += 1 
    coef2[2] -= 1
    plotline(coef, 'b', lw=2)
    plotline(coef1, 'b', ls='dashed')
    plotline(coef2, 'b', ls='dashed')

    if support_vectors != None:
        circle_out(support_vectors[:,0], support_vectors[:,1], s=100)


from pylab import *

X = array([[2.0,  2.0, 1.0, 1.0],               
              [1.0, -1.0, 1.0, -1.0]])

Y = array([[4.0, 5.0,  5.0, 4.0],
              [1.0, 1.0, -1.0, -1.0]])

data = hstack((X,Y)).T
label = hstack((zeros(X.shape[1]), ones(Y.shape[1])))

from sklearn.svm import SVC

clf = SVC(kernel='linear')
clf.fit(data, label)

coef = [clf.coef_[0,0], clf.coef_[0,1], clf.intercept_[0]]
scatter(data[:,0], data[:,1], c=label)
plotSVM(coef, clf.support_vectors_)
show()
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3 Comments

First, thank you for a complete example. But the implementation is done with sklearn which is not the module I'm working with. I'm working with shogun and use the class LibSVM. So I looked at the given example but I can't figure out what clf.coef_ means in terms of the properties of LibSVM. After training we have the alphas libsvm.get_alphas() and can get the w out of that by sum(alpha*label*support_vector). I'm sorry if I wasn't clear the first time, but I really try to understand SVM by reproducing the numbers/vectors etc.
So my question is: how to plot the hyperplane, working with shogun :)
That's a good example code... I'm curious why you use this hstack function as the output of hstack array of arrays, and array with 0/1 can be set as parameters of SVC directly.
0 
from pylab import *

def __intersect(rect, line):
    l = []
    xmin,xmax,ymin,ymax = rect
    a,b,c = line

    assert a!=0 or b!=0

    if a == 0:
        y = -c/b
        if y<=ymax and y>=ymin:
            l.append((xmin, y))
            l.append((xmax, y))
        return l
    if b == 0:
        x = -c/a
        if x<=xmax and x>=xmin:
            l.append((x, ymin))
            l.append((x, ymax))
        return l

    k = -a/b
    m = -c/b
    for x in (xmin, xmax):
        y = k*x+m
        if y<=ymax and y>= ymin:
            l.append((x,y))

    k = -b/a
    m = -c/a
    for y in (ymin, ymax):
        x = k*y+m
        if x<=xmax and y>= xmin and len(l) < 2:
            l.append((x,y))
    return l


def plotLine(coef, *args, **kwargs):
    '''plot line: y=a*x+b or a*x+b*y+c=0'''
    coef = float64(coef[:])
    assert len(coef)==2 or len(coef)==3
    if len(coef) == 2:
        a, b, c = coef[0], -1., coef[1]
    elif len(coef) == 3:
        a, b, c = coef
    ax = gca()

    limits = ax.axis()
    print limits
    points = __intersect(limits, (a,b,c))
    print points
    if len(points) == 2:
        pts = array(points)
        ax.plot(pts[:,0], pts[:,1], *args, **kwargs)
        ax.axis(limits)
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1 Comment

I'm sorry, but I don't understand. Where do you use any of the outcome of the SVM in your answer to plot the hyperplane?

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