mhjensen
63 lines
1.2 KiB
Python
63 lines
1.2 KiB
Python
import numpy as np
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import pandas as pd
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from IPython.display import display
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import matplotlib.pyplot as plt
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n = 1000
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mean = (-1, 2)
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cov = [[4, 2], [2, 2]]
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X = np.random.multivariate_normal(mean, cov, n)
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df = pd.DataFrame(X)
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# Pandas does the centering for us
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df = df -df.mean()
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print("Centered covariance with Pandas")
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covarianceX = df.cov()
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print(covarianceX)
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# we center it ourselves
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X_centered = X - X.mean(axis=0)
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print("Centered covariance using numpy")
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print(np.cov(X_centered.T))
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# extract the relevant columns from the centered design matrix
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x = X_centered[:,[0]]
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y = X_centered[:,[1]]
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Cov = np.zeros((2,2))
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cov_xy = np.sum(x.T@y)/(n-1.0)
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cov_xx = np.sum(x.T@x)/(n-1.0)
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cov_yy = np.sum(y.T@y)/(n-1.0)
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Cov[0,0]= cov_xx
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Cov[1,1]= cov_yy
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Cov[0,1]= cov_xy
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Cov[1,0]= Cov[0,1]
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print("Centered covariance using own code")
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print(Cov)
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plt.plot(x, y, 'x')
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plt.axis('equal')
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plt.show()
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"""
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#Now we do an SVD
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U, s, V = np.linalg.svd(X_centered)
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c1 = V.T[:, 0]
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c2 = V.T[:, 1]
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W2 = V.T[:, :2]
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X2D = X_centered.dot(W2)
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#thereafter we do a PCA with Scikit-learn
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from sklearn.decomposition import PCA
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pca = PCA(n_components = 2)
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X2Dsl = pca.fit_transform(X)
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print("Check that we get the same")
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print(X2D-X2Dsl)
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print(pca.components_.T[:, 0])
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"""
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