为什么我的 PCA 和来自 sklearn 的 PCA 得到不同的结果？

Question

I tried to use the PCA provided in "machine learning in action", but I found that the results obtained by it are not the same as those obtained by the PCA in sklearn. I don't quite understand what is going on.

Below is my code:

import numpy as np
from sklearn.decomposition import PCA

x = np.array([
    [1,2,3,4,5, 0],
    [0.6,0.7,0.8,0.9,0.10, 0],
    [110,120,130,140,150, 0]
])

def my_pca(data, dim):
    remove_mean = data - data.mean(axis=0)
    cov_data = np.cov(remove_mean, rowvar=0)
    eig_val, eig_vec = np.linalg.eig(np.mat(cov_data))
    sorted_eig_val = np.argsort(eig_val)
    eig_index = sorted_eig_val[:-(dim+1):-1]
    transfer = eig_vec[:,eig_index]
    low_dim = remove_mean * transfer
    return np.array(low_dim, dtype=float)

pca = PCA(n_components = 3)
pca.fit(x)
new_x = pca.transform(x)
print("sklearn")
print(new_x)

new_x = my_pca(x, 3)
print("my")
print(new_x)

Output:

sklearn
[[-9.32494230e+01  1.46120285e+00  2.37676120e-15]
 [-9.89004904e+01 -1.43283197e+00  2.98143675e-14]
 [ 1.92149913e+02 -2.83708789e-02  2.81307176e-15]]

my
[[ 9.32494230e+01 -1.46120285e+00  7.39333927e-14]
 [ 9.89004904e+01  1.43283197e+00 -7.01760428e-14]
 [-1.92149913e+02  2.83708789e-02  1.84375626e-14]]

Answer 1

The issue relates to your function, in particular the part where you calculate your eigenvector and eigenvalues:

eig_val, eig_vec = np.linalg.eig(np.mat(cov_data))

It appears that ScitKit learn uses "eigh" instead of "eig", so if you change the code snippet from np.linalg.eig to np.linalg.eigh, you should get the same results.