此範例是展示如何使用 RBF Kernel 之非線性 SVC 去做二元分類,去預測出 XOR 的輸入分佈並用 Color Map 去繪製出分類的決策邊界及區域。
引入函式如下:
numpy
: 產生陣列數值
matplotlib.pyplot
: 用來繪製影像
sklearn.svm
: SVM 支持向量機之演算法物件
import numpy as npimport matplotlib.pyplot as pltfrom sklearn import svm
xx, yy = np.meshgrid(np.linspace(-3, 3, 500),np.linspace(-3, 3, 500))np.random.seed(0)X = np.random.randn(300, 2)Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)
利用np.meshgrid
生成網格採樣點,再利用np.random.randn()
產生隨機的資料點X,接著利用np.logical_xor
對隨機生成之資料點做 xor 的分類產生Y。
# fit the modelclf = svm.NuSVC()clf.fit(X, Y)
svm.NuSVC
: 與 svm.SVC
類似,但是多了可以控制支持向量(Support Vector)個數之參數
# plot the decision function for each datapoint on the gridZ = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)plt.imshow(Z, interpolation='nearest',extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',origin='lower', cmap=plt.cm.PuOr_r)contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,linetypes='--')plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,edgecolors='k')plt.xticks(())plt.yticks(())plt.axis([-3, 3, -3, 3])plt.show()
最後繪製出非線性之決策邊界及資料點分布位置,繪圖方式可參考 EX7: SVM-Kernels 之解說。
下方為非線性分割之結果圖 :
Python source code: plot_svm_nonlinear.py
https://scikit-learn.org/stable/_downloads/plot_svm_nonlinear.py
iPython source code: plot_svm_nonlinear.ipynb
https://scikit-learn.org/stable/_downloads/plot_svm_nonlinear.ipynb
"""==============Non-linear SVM==============Perform binary classification using non-linear SVCwith RBF kernel. The target to predict is a XOR of theinputs.The color map illustrates the decision function learned by the SVC."""print(__doc__)import numpy as npimport matplotlib.pyplot as pltfrom sklearn import svmxx, yy = np.meshgrid(np.linspace(-3, 3, 500),np.linspace(-3, 3, 500))np.random.seed(0)X = np.random.randn(300, 2)Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)# fit the modelclf = svm.NuSVC()clf.fit(X, Y)# plot the decision function for each datapoint on the gridZ = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)plt.imshow(Z, interpolation='nearest',extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',origin='lower', cmap=plt.cm.PuOr_r)contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,linetypes='--')plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,edgecolors='k')plt.xticks(())plt.yticks(())plt.axis([-3, 3, -3, 3])plt.show()