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支持向量機
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。
(一)引入函式庫
引入函式如下:
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numpy: 產生陣列數值 - 2.
matplotlib.pyplot: 用來繪製影像 - 3.
sklearn.svm: SVM 支持向量機之演算法物件
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn import svm
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xx, yy = np.meshgrid(np.linspace(-3, 3, 500),
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np.linspace(-3, 3, 500))
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np.random.seed(0)
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X = np.random.randn(300, 2)
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Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)
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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。(二)SVM Model
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# fit the model
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clf = svm.NuSVC()
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clf.fit(X, Y)
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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1
# plot the decision function for each datapoint on the grid
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Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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plt.imshow(Z, interpolation='nearest',
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extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',
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origin='lower', cmap=plt.cm.PuOr_r)
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contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,
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linetypes='--')
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plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,
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edgecolors='k')
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plt.xticks(())
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plt.yticks(())
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plt.axis([-3, 3, -3, 3])
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plt.show()
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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 :
Non-linear
(三)完整程式碼
Python source code: plot_svm_nonlinear.py
iPython source code: plot_svm_nonlinear.ipynb
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"""
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==============
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Non-linear SVM
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==============
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Perform binary classification using non-linear SVC
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with RBF kernel. The target to predict is a XOR of the
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inputs.
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The color map illustrates the decision function learned by the SVC.
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"""
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print(__doc__)
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn import svm
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xx, yy = np.meshgrid(np.linspace(-3, 3, 500),
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np.linspace(-3, 3, 500))
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np.random.seed(0)
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X = np.random.randn(300, 2)
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Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)
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# fit the model
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clf = svm.NuSVC()
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clf.fit(X, Y)
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# plot the decision function for each datapoint on the grid
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Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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plt.imshow(Z, interpolation='nearest',
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extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',
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origin='lower', cmap=plt.cm.PuOr_r)
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contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,
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linetypes='--')
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plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,
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edgecolors='k')
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plt.xticks(())
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plt.yticks(())
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plt.axis([-3, 3, -3, 3])
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plt.show()
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Last modified 2yr ago
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