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 npimport matplotlib.pyplot as pltimport pandas as pdfrom sklearn.svm import SVCdef 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    00.423363    11.054677   00.406704    7.067335    10.667394    12.741452   0-2.460150   6.866805    10.569411    9.548755    0-0.026632   10.427743   00.850433    6.920334    11.347183    13.175500   01.176813    3.167020    1-1.781871   9.097953    0-0.566606   5.749003    10.931635    1.589505    1-0.024205   6.151823    1-0.036453   2.690988    1-0.196949   0.444165    11.014459    5.754399    11.985298    3.230619    1-1.693453   -0.557540   1-0.576525   11.778922   0-0.346811   -1.678730   1-2.124484   2.672471    11.217916    9.597015    0-0.733928   9.098687    0-3.642001   -1.618087   10.315985    3.523953    11.416614    9.619232    0-0.386323   3.989286    10.556921    8.294984    11.224863    11.587360   0-1.347803   -2.406051   11.196604    4.951851    10.275221    9.543647    00.470575    9.332488    0-1.889567   9.542662    0-1.527893   12.150579   0-1.185247   11.309318   0-0.445678   3.297303    11.042222    6.105155    1-0.618787   10.320986   01.152083    0.548467    10.828534    2.676045    1-1.237728   10.549033   0-0.683565   -2.166125   10.229456    5.921938    1-0.959885   11.555336   00.492911    10.993324   00.184992    8.721488    0-0.355715   10.325976   0-0.397822   8.058397    00.824839    13.730343   01.507278    5.027866    10.099671    6.835839    1-0.344008   10.717485   01.785928    7.718645    1-0.918801   11.560217   0-0.364009   4.747300    1-0.841722   4.119083    10.490426    1.960539    1-0.007194   9.075792    00.356107    12.447863   00.342578    12.281162   0-0.810823   -1.466018   12.530777    6.476801    11.296683    11.607559   00.475487    12.040035   0-0.783277   11.009725   00.074798    11.023650   0-1.337472   0.468339    1-0.102781   13.763651   0-0.147324   2.874846    10.518389    9.887035    01.015399    7.571882    0-1.658086   -0.027255   11.319944    2.171228    12.056216    5.019981    1-0.851633   4.375691    1-1.510047   6.061992    0-1.076637   -3.181888   11.821096    10.283990   03.010150    8.401766    1-1.099458   1.688274    1-0.834872   -1.733869   1-0.846637   3.849075    11.400102    12.628781   01.752842    5.468166    10.078557    0.059736    10.089392    -0.715300   11.825662    12.693808   00.197445    9.744638    00.126117    0.922311    1-0.679797   1.220530    10.677983    2.556666    10.761349    10.693862   0-2.168791   0.143632    11.388610    9.341997    00.317029    14.739025   0