支持向量机理论可参考我上一片文章：https://www.jianshu.com/p/5ec5162fe8f3
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()
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
class opt_struct:
def __init__(self, data_matin, class_labels, C, toler):
self.X = data_matin
self.label_mat = class_labels
self.C = C
self.tol = toler
self.m = shape(data_matin)[0]
self.alphas = mat(zeros((self.m, 1)))
self.b = 0
self.e_cache = mat(zeros((self.m, 2)))
def calc_ek(os, k):
fxk = float((multiply(os.alphas, os.label_mat).T) * (os.X * os.X[k, :].T)) + os.b
ek = fxk - os.label_mat[k]
return fxk,ek
def select_j(os, i, ei):
maxk = -1
max_delta_e = 0
ej = 0
os.e_cache[i] = [1, ei]
valid_e_cache_list = nonzero(os.e_cache[0].A)[0]
if(len(valid_e_cache_list)) > 1:
for k in valid_e_cache_list:
if (k == 1):
continue
fxk,ek = os.calc_ek(k)
delta_e = abs(ei - ek)
if(delta_e > max_delta_e):
maxk = k
max_delta_e = delta_e
ej = ek
return maxk, ej
else:
j = select_j_rand(i, os.m)
fj,ej = os.calc_ek(j)
return j, ej
def update_ek(os, k):
fxk,ek = os.calc_ek(k)
os.e_cache[k] = [1, ek]
def innert(os, i):
fxi,ei = os.calc_ek(i)
if(((os.label_mat[i] * ei < -os.tol) and (os.alphas[i] < os.C)) or\
((os.label_mat[i] * ei > os.tol) and (os.alphas[i] > 0))):
#if((os.label_mat[i] * (fxi - 2 * os.b) <= 1 and os.alphas[i] < os.C)\
# or (os.label_mat[i] * (fxi - 2 * os.b) >= 1 and os.alphas[i] > 0)\
# or (os.label_mat[i] * (fxi - 2 * os.b) == 1 and (os.alphas[i] == 0 or os.alphas[i] == os.C))):
j,ej = os.select_j(i, ei)
alpha_i_old = os.alphas[i].copy()
alpha_j_old = os.alphas[j].copy()
if(os.label_mat[i] != os.label_mat[j]):
L = max(0, os.alphas[j] - os.alphas[i])
H = min(os.C, os.C + os.alphas[j] - os.alphas[i])
else:
L = max(0, os.alphas[j] + os.alphas[i] - os.C)
H = min(os.C, os.alphas[j] + os.alphas[i])
if(L == H):
print("L == H")
return 0
eta = 2 * os.X[i, :] * os.X[j, :].T - os.X[i, :] * os.X[i, :].T - os.X[j, :] * os.X[j, :].T
if(eta >= 0):
print("eta >= 0")
return 0
os.alphas[j] = alpha_j_old - (os.label_mat[j] * (ei - ej)) * 1.0 / eta
os.alphas[j] = clip_alpha(os.alphas[j], H, L)
os.update_ek(j)
if(abs(os.alphas[j] - alpha_j_old) < 0.00001):
print("j not move")
return 0
os.alphas[i] = alpha_i_old + os.label_mat[i] * os.label_mat[j] * (alpha_j_old - os.alphas[j])
os.update_ek(i)
b1 = os.b - ei - os.label_mat[i] * (os.alphas[i] - alpha_i_old) * (os.alphas[i, :] * os.alphas[i, :].T) -\
os.label_mat[j] * (os.alphas[j] - alpha_j_old) * (os.alphas[i, :] * os.alphas[j, :].T)
b2 = os.b - ej - os.label_mat[j] * (os.alphas[i] - alpha_i_old) * (os.alphas[i, :] * os.alphas[j, :].T) -\
os.label_mat[j] * (os.alphas[j, :] - alpha_j_old) * (os.alphas[j, :] * os.alphas[j, :])
if(os.alphas[i] > 0 and os.alphas[i] < os.C):
os.b = b1
elif(os.alphas[j] > 0 and os.alphas[j] < os.C):
os.b = b2
else:
os.b = (b1 + b2) * 1.0 / 2
return 1
else:
return 0
def smop(data_mat_in, class_labels, C, toler, max_iter):
os = opt_struct(mat(data_mat_in), mat(class_labels).transpose(), C, toler)
iter = 0
entire_set = True
alpha_paris_changed = 0
while((iter < max_iter) and (alpha_paris_changed > 0) or (entire_set)):
alpha_paris_changed = 0
if entire_set:
for i in range(os.m):
alpha_paris_changed += innert(os, i)
iter += 1
else:
non_bound_is = nonzero((os.alphas.A > 0) * (os.alphas.A < C))[0]
for i in non_bound_is:
alpha_paris_changed += innert(os, i)
iter += 1
if entire_set:
entire_set = False
elif(alpha_paris_changed == 0):
entire_set = True
return os.b, os.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 = smop(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()
在opt_struct类中的成员函数select_j，选择误差值最大的点进行更新拉格朗日系数是由式子：
3.PNG
决定的，同时也说明了由决策函数计算得到的值与实际值偏差太大，则更加需要调整决策函数的权值，分类决策函数基本模型如下：
4.PNG
权值与拉格朗日系数与权值的关系：
5.PNG
由权值与拉格朗日系数的关系可以得出，如果权值需要更新则拉格朗日的系数也需要更新。
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
可以看出优化版的与简化版的稍有不同，但是速度明显提高了许多，支持向量的点也多一些。