ML之MIC：利用有无噪音的正余弦函数理解相关性指标的不同(多图绘制Pearson系数、最大信息系数MIC)

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4. #ML之MIC：利用有无噪音的正余弦函数理解相关性指标的不同(多图绘制Pearson系数、最大信息系数MIC)
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6. import numpy as np
7. import matplotlib.pyplot as plt
8. from minepy import MINE
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10. 
11. def mysubplot(x, y, numRows, numCols, plotNum,
12.               xlim=(-4, 4), ylim=(-4, 4)):
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14.     r = np.around(np.corrcoef(x, y)[0, 1], 1)
15.     mine = MINE(alpha=0.6, c=15)
16.     mine.compute_score(x, y)
17.     mic = np.around(mine.mic(), 1)
18.     ax = plt.subplot(numRows, numCols, plotNum,
19.                      xlim=xlim, ylim=ylim)
20.     ax.set_title('Pearson r=%.1f\nMIC=%.1f' % (r, mic),fontsize=10)
21.     ax.set_frame_on(False)
22.     ax.axes.get_xaxis().set_visible(False)
23.     ax.axes.get_yaxis().set_visible(False)
24.     ax.plot(x, y, ',')
25.     ax.set_xticks([])
26.     ax.set_yticks([])
27. return ax
28. 
29. def rotation(xy, t):
30. return np.dot(xy, [[np.cos(t), -np.sin(t)],
31.                        [np.sin(t), np.cos(t)]])
32. 
33. def mvnormal(n=1000):
34.     cors = [1.0, 0.8, 0.4, 0.0, -0.4, -0.8, -1.0]
35. for i, cor in enumerate(cors):
36.         cov = [[1, cor],[cor, 1]]
37.         xy = np.random.multivariate_normal([0, 0], cov, n)
38.         mysubplot(xy[:, 0], xy[:, 1], 3, 7, i+1)
39. 
40. def rotnormal(n=1000):
41.     ts = [0, np.pi/12, np.pi/6, np.pi/4, np.pi/2-np.pi/6,
42.           np.pi/2-np.pi/12, np.pi/2]
43.     cov = [[1, 1],[1, 1]]
44.     xy = np.random.multivariate_normal([0, 0], cov, n)
45. for i, t in enumerate(ts):
46.         xy_r = rotation(xy, t)
47.         mysubplot(xy_r[:, 0], xy_r[:, 1], 3, 7, i+8)
48. 
49. def others(n=1000):
50.     x = np.random.uniform(-1, 1, n)
51.     y = 4*(x**2-0.5)**2 + np.random.uniform(-1, 1, n)/3
52.     mysubplot(x, y, 3, 7, 15, (-1, 1), (-1/3, 1+1/3))
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54.     y = np.random.uniform(-1, 1, n)
55.     xy = np.concatenate((x.reshape(-1, 1), y.reshape(-1, 1)), axis=1)
56.     xy = rotation(xy, -np.pi/8)
57.     lim = np.sqrt(2+np.sqrt(2)) / np.sqrt(2)
58.     mysubplot(xy[:, 0], xy[:, 1], 3, 7, 16, (-lim, lim), (-lim, lim))
59. 
60.     xy = rotation(xy, -np.pi/8)
61.     lim = np.sqrt(2)
62.     mysubplot(xy[:, 0], xy[:, 1], 3, 7, 17, (-lim, lim), (-lim, lim))
63. 
64.     y = 2*x**2 + np.random.uniform(-1, 1, n)
65.     mysubplot(x, y, 3, 7, 18, (-1, 1), (-1, 3))
66. 
67.     y = (x**2 + np.random.uniform(0, 0.5, n)) * \
68.         np.array([-1, 1])[np.random.random_integers(0, 1, size=n)]
69.     mysubplot(x, y, 3, 7, 19, (-1.5, 1.5), (-1.5, 1.5))
70. 
71.     y = np.cos(x * np.pi) + np.random.uniform(0, 1/8, n)
72.     x = np.sin(x * np.pi) + np.random.uniform(0, 1/8, n)
73.     mysubplot(x, y, 3, 7, 20, (-1.5, 1.5), (-1.5, 1.5))
74. 
75.     xy1 = np.random.multivariate_normal([3, 3], [[1, 0], [0, 1]], int(n/4))
76.     xy2 = np.random.multivariate_normal([-3, 3], [[1, 0], [0, 1]], int(n/4))
77.     xy3 = np.random.multivariate_normal([-3, -3], [[1, 0], [0, 1]], int(n/4))
78.     xy4 = np.random.multivariate_normal([3, -3], [[1, 0], [0, 1]], int(n/4))
79.     xy = np.concatenate((xy1, xy2, xy3, xy4), axis=0)
80.     mysubplot(xy[:, 0], xy[:, 1], 3, 7, 21, (-7, 7), (-7, 7))
81. 
82. plt.figure(facecolor='white')
83. mvnormal(n=800)
84. rotnormal(n=200)
85. others(n=800)
86. plt.tight_layout()
87. 
88. plt.suptitle('Understand the difference of correlation index (Pearson VS MIC)')
89. plt.show()
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