如何用python绘制超平面支持向量机？

Question

我的第一个问题，请你耐心听我说：）

我在Python中使用Shogun工具箱来处理SVM。为了更好地理解支持向量机，我先做了一些实验，用Python语言编写了一些数据点来线性分离。我使用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]])

在用给定的数据训练支持向量机之后，我可以检索它的偏差（get_bias()）、支持向量（get_support_vectors()）和其他属性。我做不到的是绘制直线/超平面。我知道超平面的方程是y=wx + b，但是如何写下/画出这个来在我的图中看到它。在

Answer 1

一个完整的例子

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()

Answer 2

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)