# encoding:utf8
from numpy import *
import numpy as np
import matplotlib.pyplot as plt
def load_data(filename):
dataset, labels = [], []
with open(filename, 'r') as f:
for line in f:
x, y, label = [float(i) for i in line.strip().split()]
dataset.append([x, y])
labels.append(label)
return dataset, labels
def clip(alpha, L, H):
''' 修建alpha的值到L和H之间.
'''
if alpha < L:
return L
elif alpha > H:
return H
else:
return alpha
def select_j(i, m):
''' 在m中随机选择除了i之外剩余的数
'''
l = list(range(m))
seq = l[: i] + l[i + 1:]
return random.choice(seq)
def get_w(alphas, dataset, labels):
''' 通过已知数据点和拉格朗日乘子获得分割超平面参数w
'''
alphas, dataset, labels = np.array(alphas), np.array(dataset), np.array(labels)
# w = Σ ai*yi* xi
w = np.dot(dataset.T, alphas * labels)
return w.tolist()
def simple_smo(dataset, labels, C, max_iter):
''' 简化版SMO算法实现，未使用启发式方法对alpha对进行选择.
:param dataset: 所有特征数据向量
:param labels: 所有的数据标签
:param C: 软间隔常数, 0 <= alpha_i <= C
:param max_iter: 外层循环最大迭代次数
'''
dataset = np.array(dataset)
m, n = dataset.shape
labels = np.array(labels)
# 初始化参数
alphas = np.zeros(m)
b = 0
it = 0
def f(x):
"SVM分类器函数 y = w^Tx + b"
# Kernel function vector.
x = np.matrix(x).T
data = np.matrix(dataset)
ks = data * x
# Predictive value.
wx = np.matrix(alphas * labels) * ks
fx = wx + b
return fx[0, 0]
while it < max_iter:
pair_changed = 0
for i in range(m):
a_i, x_i, y_i = alphas[i], dataset[i], labels[i]
fx_i = f(x_i)
E_i = fx_i - y_i
j = select_j(i, m)
a_j, x_j, y_j = alphas[j], dataset[j], labels[j]
fx_j = f(x_j)
E_j = fx_j - y_j
K_ii, K_jj, K_ij = np.dot(x_i, x_i), np.dot(x_j, x_j), np.dot(x_i, x_j)
eta = K_ii + K_jj - 2 * K_ij
if eta <= 0:
print('WARNING eta <= 0')
continue
# 获取更新的alpha对
a_i_old, a_j_old = a_i, a_j
a_j_new = a_j_old + y_j * (E_i - E_j) / eta
# 对alpha进行修剪
if y_i != y_j:
L = max(0, a_j_old - a_i_old)
H = min(C, C + a_j_old - a_i_old)
else:
L = max(0, a_i_old + a_j_old - C)
H = min(C, a_j_old + a_i_old)
a_j_new = clip(a_j_new, L, H)
a_i_new = a_i_old + y_i * y_j * (a_j_old - a_j_new)
if abs(a_j_new - a_j_old) < 0.00001:
# print('WARNING alpha_j not moving enough')
continue
alphas[i], alphas[j] = a_i_new, a_j_new
# 更新阈值b
b_i = -E_i - y_i * K_ii * (a_i_new - a_i_old) - y_j * K_ij * (a_j_new - a_j_old) + b
b_j = -E_j - y_i * K_ij * (a_i_new - a_i_old) - y_j * K_jj * (a_j_new - a_j_old) + b
if 0 < a_i_new < C:
b = b_i
elif 0 < a_j_new < C:
b = b_j
else:
b = (b_i + b_j) / 2
pair_changed += 1
print('INFO iteration:{} i:{} pair_changed:{}'.format(it, i, pair_changed))
it += 1
if pair_changed == 0:
it += 1
else:
it = 0
print('iteration number: {}'.format(it))
return alphas, b
if '__main__' == __name__:
# 加载训练数据
dataset, labels = load_data('data/testSet-svm.txt')
# 使用简化版SMO算法优化SVM
alphas, b = simple_smo(dataset, labels, 0.6, 40)
# 分类数据点
classified_pts = {'+1': [], '-1': []}
for point, label in zip(dataset, labels):
if label == 1.0:
classified_pts['+1'].append(point)
else:
classified_pts['-1'].append(point)
fig = plt.figure()
ax = fig.add_subplot(111)
# 绘制数据点
for label, pts in classified_pts.items():
pts = np.array(pts)
ax.scatter(pts[:, 0], pts[:, 1], label=label)
# 绘制分割线
w = get_w(alphas, dataset, labels)
x1, _ = max(dataset, key=lambda x: x[0])
x2, _ = min(dataset, key=lambda x: x[0])
a1, a2 = w
# x,y 在分隔面上，满足 W * X +b = a1 * x + a2 *y +b = 0
y1, y2 = (-b - a1 * x1) / a2, (-b - a1 * x2) / a2
ax.plot([x1, x2], [y1, y2])
# 绘制支持向量
for i, alpha in enumerate(alphas):
if abs(alpha) > 1e-3:
x, y = dataset[i]
ax.scatter([x], [y], s=150, c='none', alpha=0.7,
linewidth=1.5, edgecolor='#AB3319')
plt.show()
