支持向量机的理论这里就不介绍了，可参考《统计学习方法》这本书，书上已经把整个过程写得很详细。如果觉得看书太枯燥，花费时间多，可以参考这边博文https://blog.csdn.net/v_JULY_v/article/details/7624837，写得非常好，通俗易懂。下面，是我参考《机器学习实战》这本书上代码写得支持向量机实现代码。
from numpy import *
import numpy as np
import matplotlib.pyplot as plt
def load_set_data(file_name):
data_mat = []
label_mat = []
n = 0
fr = open(file_name)
for line in fr.readlines():
line_arr = line.strip().split("\t")
data_mat.append([float(line_arr[0]), float(line_arr[1])])
label_mat.append(float(line_arr[2]))
n += 1
return data_mat, label_mat, n
def select_j_rand(i, m):
j = i
while (j == i):
j = int(random.uniform(0, m))
return j
def clip_alpha(aj, H, L):
if aj > H:
aj = H
if aj < L:
aj = L
return aj
def smo_simple(data_matin, class_labele, C, toler, max_iter):
data_matrix = mat(data_matin) #将输入列表转成矩阵
label_mat = mat(class_labele).transpose() #将训练数据转成列向量
b = 0
m,n = shape(data_matrix)
alphas = mat(zeros((m, 1)))
iter = 0
while(iter < max_iter):
alpha_pirs_change = 0
for i in range(m):
fxi = float(multiply(alphas, label_mat).T * (data_matrix * (data_matrix[i, :].T))) + b
ei = fxi - float(label_mat[i])
#if ((label_mat[i] * ei < -toler) and (alphas[i] < C)) or \
# ((label_mat[i] * ei > toler) and \
# (alphas[i] > 0)):
if((label_mat[i] * (fxi - 2 * b) <= 1 and alphas[i] < C)\
or (label_mat[i] * (fxi - 2 * b) >= 1 and alphas[i] > 0)\
or (label_mat[i] * (fxi - 2 * b) == 1 and (alphas[i] == 0 or alphas[i] == C))):
j = select_j_rand(i, m) #随机选择aj且i != j，相当于随机选择ai和aj
fxj = float(multiply(alphas, label_mat).T * \
(data_matrix * data_matrix[j, :].T)) + b
ej = fxj - float(label_mat[j])
alpha_iold = alphas[i].copy() #保存alphai更新前的值
alpha_jold = alphas[j].copy() #保存alphaj更新前的值
#求解alphaj的上下边界
if (label_mat[i] != label_mat[j]):
L = max(0, alpha_jold - alpha_iold)
H = min(C, C + alpha_jold + alpha_iold)
else:
L = max(0, alpha_jold + alpha_iold - C)
H = min(C, alpha_iold + alpha_jold)
if (L == H):
print("L == H")
continue
eta = 2 * data_matrix[i, :] * data_matrix[j, :].T \
- data_matrix[i, :] * data_matrix[i, :].T - data_matrix[j, :] * data_matrix[j, :].T
if (eta > 0):
print("eta > 0")
continue
alphas[j] = alpha_jold - (label_mat[j] * (ei - ej) * 1.0 / eta)
alphas[j] = clip_alpha(alphas[j], H, L)
if (abs(alphas[j] - alpha_jold) < 0.00001):
print("j not moving enough")
continue
alphas[i] = alpha_iold + (label_mat[i] * label_mat[j] * (alpha_jold - alphas[j]))
b1 = b - ei - label_mat[i] * (alphas[i] - alpha_iold) * (data_matrix[i, :] * data_matrix[i, :].T)\
- label_mat[j] * (alphas[j] - alpha_jold) * (data_matrix[i, :] * data_matrix[j, :].T)
b2 = b - ej - label_mat[i] * (alphas[i] - alpha_iold) * (data_matrix[i, :] * data_matrix[j, :].T)\
- label_mat[j] * (alphas[j] - alpha_jold) * (data_matrix[j, :] * data_matrix[j, :].T)
if (alphas[i] > 0 and alphas[i] < C):
b = b1
elif (alphas[j] > 0 and alphas[j] < C):
b = b2
else:
b = (b1 + b2) / 2.0
alpha_pirs_change += 1
print("iter: %d i: %d, paris changed % d" % (iter, i, alpha_pirs_change))
if (alpha_pirs_change == 0):
iter += 1
else:
iter = 0
print("iteration number: %d" % iter)
return b,alphas
def show_experiment_plot(alphas, data_list_in, label_list_in, b, n):
data_arr_in = array(data_list_in)
label_arr_in = array(label_list_in)
alphas_arr = alphas.getA()
data_mat = mat(data_list_in)
label_mat = mat(label_list_in).transpose()
i = 0
weights = zeros((2, 1))
while(i < n):
if(label_arr_in[i] == -1):
plt.plot(data_arr_in[i, 0], data_arr_in[i, 1], "ob")
elif(label_arr_in[i] == 1):
plt.plot(data_arr_in[i, 0], data_arr_in[i, 1], "or")
if(alphas_arr[i] > 0):
plt.plot(data_arr_in[i, 0], data_arr_in[i, 1], "oy")
weights += multiply(alphas[i] * label_mat[i], data_mat[i, :].T)
i += 1
x = arange(-2, 12, 0.1)
y = []
for k in x:
y.append(float(-b - weights[0] * k) / weights[1])
plt.plot(x, y, '-g')
plt.xlabel("X")
plt.ylabel("Y")
plt.show()
def main():
data_list,label_list, n = load_set_data("test_set.txt")
b,alphas = smo_simple(data_list, label_list, 0.6, 0.001, 40)
b_data = array(b)[0][0]
show_experiment_plot(alphas, data_list, label_list, b_data, n)
main()
代码中被注释的部分是《机器学习实战》这本书的写法，看了很久还是没有搞明白作者为什么这么写，如果哪位大神知道，还请说一下，大家好互相学习。根据KKT条件我自己重现实现了更新alphas的条件判断。
特征到结果的输出函数：
ui = w.x - b
其中w，x和ui均为向量
2.PNG
也就是说，当没有满足KKT条件时，则需要更新alphas的值。
实验数据：
3.542485 1.977398 -1
3.018896 2.556416 -1
7.551510 -1.580030 1
2.114999 -0.004466 -1
8.127113 1.274372 1
7.108772 -0.986906 1
8.610639 2.046708 1
2.326297 0.265213 -1
3.634009 1.730537 -1
0.341367 -0.894998 -1
3.125951 0.293251 -1
2.123252 -0.783563 -1
0.887835 -2.797792 -1
7.139979 -2.329896 1
1.696414 -1.212496 -1
8.117032 0.623493 1
8.497162 -0.266649 1
4.658191 3.507396 -1
8.197181 1.545132 1
1.208047 0.213100 -1
1.928486 -0.321870 -1
2.175808 -0.014527 -1
7.886608 0.461755 1
3.223038 -0.552392 -1
3.628502 2.190585 -1
7.407860 -0.121961 1
7.286357 0.251077 1
2.301095 -0.533988 -1
-0.232542 -0.547690 -1
3.457096 -0.082216 -1
3.023938 -0.057392 -1
8.015003 0.885325 1
8.991748 0.923154 1
7.916831 -1.781735 1
7.616862 -0.217958 1
2.450939 0.744967 -1
7.270337 -2.507834 1
1.749721 -0.961902 -1
1.803111 -0.176349 -1
8.804461 3.044301 1
1.231257 -0.568573 -1
2.074915 1.410550 -1
-0.743036 -1.736103 -1
3.536555 3.964960 -1
8.410143 0.025606 1
7.382988 -0.478764 1
6.960661 -0.245353 1
8.234460 0.701868 1
8.168618 -0.903835 1
1.534187 -0.622492 -1
9.229518 2.066088 1
7.886242 0.191813 1
2.893743 -1.643468 -1
1.870457 -1.040420 -1
5.286862 -2.358286 1
6.080573 0.418886 1
2.544314 1.714165 -1
6.016004 -3.753712 1
0.926310 -0.564359 -1
0.870296 -0.109952 -1
2.369345 1.375695 -1
1.363782 -0.254082 -1
7.279460 -0.189572 1
1.896005 0.515080 -1
8.102154 -0.603875 1
2.529893 0.662657 -1
1.963874 -0.365233 -1
8.132048 0.785914 1
8.245938 0.372366 1
6.543888 0.433164 1
-0.236713 -5.766721 -1
8.112593 0.295839 1
9.803425 1.495167 1
1.497407 -0.552916 -1
1.336267 -1.632889 -1
9.205805 -0.586480 1
1.966279 -1.840439 -1
8.398012 1.584918 1
7.239953 -1.764292 1
7.556201 0.241185 1
9.015509 0.345019 1
8.266085 -0.230977 1
8.545620 2.788799 1
9.295969 1.346332 1
2.404234 0.570278 -1
2.037772 0.021919 -1
1.727631 -0.453143 -1
1.979395 -0.050773 -1
8.092288 -1.372433 1
1.667645 0.239204 -1
9.854303 1.365116 1
7.921057 -1.327587 1
8.500757 1.492372 1
1.339746 -0.291183 -1
3.107511 0.758367 -1
2.609525 0.902979 -1
3.263585 1.367898 -1
2.912122 -0.202359 -1
1.731786 0.589096 -1
2.387003 1.573131 -1
实验结果如下：
1.PNG
图中黄色的点是支持向量的（alphas[i] > 0对应的(xi, yi)）。实验结果表明。该算法能正确分类，效果良好。
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