ML之MIC：利用有無噪音的正余弦函數理解相關性指標的不同(多圖繪制Pearson系數、最大信息系數MIC)

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目錄

利用有無噪音的正余弦函數理解相關性指標的不同(多圖繪制Pearson系數、最大信息系數MIC)

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實現代碼

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利用有無噪音的正余弦函數理解相關性指標的不同(多圖繪制Pearson系數、最大信息系數MIC)

輸出結果

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實現代碼

#ML之MIC：利用有無噪音的正余弦函數理解相關性指標的不同(多圖繪制Pearson系數、最大信息系數MIC)import numpy as np import matplotlib.pyplot as plt from minepy import MINEdef mysubplot(x, y, numRows, numCols, plotNum,xlim=(-4, 4), ylim=(-4, 4)):r = np.around(np.corrcoef(x, y)[0, 1], 1)mine = MINE(alpha=0.6, c=15)mine.compute_score(x, y)mic = np.around(mine.mic(), 1)ax = plt.subplot(numRows, numCols, plotNum,xlim=xlim, ylim=ylim)ax.set_title('Pearson r=%.1f\nMIC=%.1f' % (r, mic),fontsize=10)ax.set_frame_on(False)ax.axes.get_xaxis().set_visible(False)ax.axes.get_yaxis().set_visible(False)ax.plot(x, y, ',')ax.set_xticks([])ax.set_yticks([])return axdef rotation(xy, t):return np.dot(xy, [[np.cos(t), -np.sin(t)],[np.sin(t), np.cos(t)]])def mvnormal(n=1000):cors = [1.0, 0.8, 0.4, 0.0, -0.4, -0.8, -1.0]for i, cor in enumerate(cors):cov = [[1, cor],[cor, 1]]xy = np.random.multivariate_normal([0, 0], cov, n)mysubplot(xy[:, 0], xy[:, 1], 3, 7, i+1)def rotnormal(n=1000):ts = [0, np.pi/12, np.pi/6, np.pi/4, np.pi/2-np.pi/6,np.pi/2-np.pi/12, np.pi/2]cov = [[1, 1],[1, 1]]xy = np.random.multivariate_normal([0, 0], cov, n)for i, t in enumerate(ts):xy_r = rotation(xy, t)mysubplot(xy_r[:, 0], xy_r[:, 1], 3, 7, i+8)def others(n=1000):x = np.random.uniform(-1, 1, n)y = 4*(x**2-0.5)**2 + np.random.uniform(-1, 1, n)/3mysubplot(x, y, 3, 7, 15, (-1, 1), (-1/3, 1+1/3))y = np.random.uniform(-1, 1, n)xy = np.concatenate((x.reshape(-1, 1), y.reshape(-1, 1)), axis=1)xy = rotation(xy, -np.pi/8)lim = np.sqrt(2+np.sqrt(2)) / np.sqrt(2)mysubplot(xy[:, 0], xy[:, 1], 3, 7, 16, (-lim, lim), (-lim, lim))xy = rotation(xy, -np.pi/8)lim = np.sqrt(2)mysubplot(xy[:, 0], xy[:, 1], 3, 7, 17, (-lim, lim), (-lim, lim))y = 2*x**2 + np.random.uniform(-1, 1, n)mysubplot(x, y, 3, 7, 18, (-1, 1), (-1, 3))y = (x**2 + np.random.uniform(0, 0.5, n)) * \np.array([-1, 1])[np.random.random_integers(0, 1, size=n)]mysubplot(x, y, 3, 7, 19, (-1.5, 1.5), (-1.5, 1.5))y = np.cos(x * np.pi) + np.random.uniform(0, 1/8, n)x = np.sin(x * np.pi) + np.random.uniform(0, 1/8, n)mysubplot(x, y, 3, 7, 20, (-1.5, 1.5), (-1.5, 1.5))xy1 = np.random.multivariate_normal([3, 3], [[1, 0], [0, 1]], int(n/4))xy2 = np.random.multivariate_normal([-3, 3], [[1, 0], [0, 1]], int(n/4))xy3 = np.random.multivariate_normal([-3, -3], [[1, 0], [0, 1]], int(n/4))xy4 = np.random.multivariate_normal([3, -3], [[1, 0], [0, 1]], int(n/4))xy = np.concatenate((xy1, xy2, xy3, xy4), axis=0)mysubplot(xy[:, 0], xy[:, 1], 3, 7, 21, (-7, 7), (-7, 7))plt.figure(facecolor='white') mvnormal(n=800) rotnormal(n=200) others(n=800) plt.tight_layout()plt.suptitle('Understand the difference of correlation index (Pearson VS MIC)') plt.show()

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