sklearn之SVM二分类
理论部分
- 线性支持向量机
- 对偶形式支持向量机
- 核函数支持向量机
- 软间隔支持向量机
- Kernel Logistic Regression
- Support Vector Regression(SVR)
使用sklearn实现的不同核函数的SVM
使用不同核函数的 SVM 用于二分类问题并可视化分类结果。
# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.svm import SVC
def bc():
data = pd.read_table(r'./data/testSet.txt', header=None, delim_whitespace=True)
print(data.info())
print(data.head())
X_train = np.array(data.loc[:][[0, 1]])
y_train = np.array(data[2])
y_train = np.where(y_train == 1, 1, -1)
x_min = X_train[:, 0].min()
x_max = X_train[:, 0].max()
y_min = X_train[:, 1].min()
y_max = X_train[:, 1].max()
'''
linear svm, poly svm, rbf svm
'''
plt.figure(figsize=(15, 15))
for fig_num, kernel in enumerate(('linear', 'poly', 'rbf')):
svm_ = SVC(kernel=kernel)
svm_.fit(X_train, y_train)
# support vectors
# plt.figure(fig_num)
# plt.clf()
plt.subplot(222 + fig_num)
plt.scatter(x = X_train[y_train == 1, 0], y = X_train[y_train == 1, 1],
s = 30, marker = 'o', color = 'yellow', zorder = 10)
plt.scatter(x = X_train[y_train == -1, 0], y = X_train[y_train == -1, 1],
s = 30, marker = 'x', color = 'blue', zorder = 10)
plt.scatter(x = [x[0] for x in svm_.support_vectors_], y = [x[1] for x in svm_.support_vectors_], s = 80, facecolors='none', zorder = 10)
print(len(svm_.support_vectors_))
plt.title(kernel)
plt.xlabel('support vectors ' + str(len(svm_.support_vectors_)))
plt.xticks([])
plt.yticks([])
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
XX, YY = np.mgrid[x_min:x_max:200j, y_min:y_max:200j]
Z = svm_.decision_function(np.c_[XX.ravel(), YY.ravel()])
Z = Z.reshape(XX.shape)
plt.pcolormesh(XX, YY, Z > 0, cmap=plt.cm.Paired)
plt.contour(XX, YY, Z, colors=['black', 'k', 'white'], linestyles=['--', '-', '--'], levels=[-.5, 0, .5])
# plot data
plt.subplot(221)
plt.title('data')
plt.scatter(x=X_train[y_train == 1, 0], y=X_train[y_train == 1, 1],
s=30, marker='o', color='red', zorder=10)
plt.scatter(x=X_train[y_train == -1, 0], y=X_train[y_train == -1, 1],
s=30, marker='x', color='blue', zorder=10)
plt.xticks([])
plt.yticks([])
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.savefig(r'./data/svm' + str(kernel) + '.jpg')
plt.show()
if __name__ == '__main__':
bc()运行结果
使用大圆圈圈出了支持向量，并且在每一个图下给出了支持向量的个数。
实验数据
-0.017612 14.053064 0
-1.395634 4.662541 1
-0.752157 6.538620 0
-1.322371 7.152853 0
0.423363 11.054677 0
0.406704 7.067335 1
0.667394 12.741452 0
-2.460150 6.866805 1
0.569411 9.548755 0
-0.026632 10.427743 0
0.850433 6.920334 1
1.347183 13.175500 0
1.176813 3.167020 1
-1.781871 9.097953 0
-0.566606 5.749003 1
0.931635 1.589505 1
-0.024205 6.151823 1
-0.036453 2.690988 1
-0.196949 0.444165 1
1.014459 5.754399 1
1.985298 3.230619 1
-1.693453 -0.557540 1
-0.576525 11.778922 0
-0.346811 -1.678730 1
-2.124484 2.672471 1
1.217916 9.597015 0
-0.733928 9.098687 0
-3.642001 -1.618087 1
0.315985 3.523953 1
1.416614 9.619232 0
-0.386323 3.989286 1
0.556921 8.294984 1
1.224863 11.587360 0
-1.347803 -2.406051 1
1.196604 4.951851 1
0.275221 9.543647 0
0.470575 9.332488 0
-1.889567 9.542662 0
-1.527893 12.150579 0
-1.185247 11.309318 0
-0.445678 3.297303 1
1.042222 6.105155 1
-0.618787 10.320986 0
1.152083 0.548467 1
0.828534 2.676045 1
-1.237728 10.549033 0
-0.683565 -2.166125 1
0.229456 5.921938 1
-0.959885 11.555336 0
0.492911 10.993324 0
0.184992 8.721488 0
-0.355715 10.325976 0
-0.397822 8.058397 0
0.824839 13.730343 0
1.507278 5.027866 1
0.099671 6.835839 1
-0.344008 10.717485 0
1.785928 7.718645 1
-0.918801 11.560217 0
-0.364009 4.747300 1
-0.841722 4.119083 1
0.490426 1.960539 1
-0.007194 9.075792 0
0.356107 12.447863 0
0.342578 12.281162 0
-0.810823 -1.466018 1
2.530777 6.476801 1
1.296683 11.607559 0
0.475487 12.040035 0
-0.783277 11.009725 0
0.074798 11.023650 0
-1.337472 0.468339 1
-0.102781 13.763651 0
-0.147324 2.874846 1
0.518389 9.887035 0
1.015399 7.571882 0
-1.658086 -0.027255 1
1.319944 2.171228 1
2.056216 5.019981 1
-0.851633 4.375691 1
-1.510047 6.061992 0
-1.076637 -3.181888 1
1.821096 10.283990 0
3.010150 8.401766 1
-1.099458 1.688274 1
-0.834872 -1.733869 1
-0.846637 3.849075 1
1.400102 12.628781 0
1.752842 5.468166 1
0.078557 0.059736 1
0.089392 -0.715300 1
1.825662 12.693808 0
0.197445 9.744638 0
0.126117 0.922311 1
-0.679797 1.220530 1
0.677983 2.556666 1
0.761349 10.693862 0
-2.168791 0.143632 1
1.388610 9.341997 0
0.317029 14.739025 0