程序示例–非線性決策邊界

我們首先對數據進行了多項式擬合，再分別使用 $\lambda =0,\lambda =1,\lambda =100$ 的批量梯度下降法（sgd）完成了訓練，獲得了非線性決策邊界：

# coding: utf-8 # logical_regression/test_non_linear_boundry.py import numpy as np import logical_regression as regression import matplotlib.pyplot as plt import matplotlib.ticker as mtick from sklearn.preprocessing import PolynomialFeaturesif __name__ == "__main__":X, y = regression.loadDataSet('data/non_linear.txt')poly = PolynomialFeatures(6)XX = poly.fit_transform(X[:,1:3])m, n = XX.shapeoptions = [{'rate': 1,'epsilon': 0.01,'theLambda': theLambda,'maxLoop': 3000,'method': 'bgd'} for theLambda in [0, 1.0, 100.0]]figures, axes = plt.subplots(1,3, sharey = True, figsize=(17,5))for idx, option in enumerate(options):result, timeConsumed = regression.gradient(XX, y, option)thetas, errors, iterationCount = resulttheta = thetas[-1]print theta, errors[-1], iterationCountax = axes[idx]# 繪制數據點title = '%s: rate=%.2f, iterationCount=%d, \n theLambda=%d, \n error=%.2f time: %.2fs' % (option['method'], option['rate'], iterationCount, option['theLambda'], errors[-1], timeConsumed)ax.set_title(title)ax.set_xlabel('X1')ax.set_ylabel('X2')for i in range(m):x = X[i].A[0]if y[i] == 1:ax.scatter(x[1], x[2], marker='*', color='black', s=50)else:ax.scatter(x[1], x[2], marker='o', color='green', s=50)# 繪制決策邊界x1Min = X[:, 1].min()x1Max = X[:, 1].max()x2Min = X[:, 2].min()x2Max = X[:, 2].max()xx1, xx2 = np.meshgrid(np.linspace(x1Min, x1Max),np.linspace(x2Min, x2Max))h = regression.sigmoid(poly.fit_transform(np.c_[xx1.ravel(), xx2.ravel()]).dot(theta))h = h.reshape(xx1.shape)ax.contour(xx1, xx2, h, [0.5], colors='b', linewidth=.5)plt.show()

程序運行結果如下：

總結

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