如何在PCA中变白矩阵 [英] How to whiten matrix in PCA

问题描述

我正在使用Python，并且已经使用本教程.

I'm working with Python and I've implemented the PCA using this tutorial.

一切正常，我进行了一次成功的协方差转换，将其转换为原始尺寸没问题.

Everything works great, I got the Covariance I did a successful transform, brought it make to the original dimensions not problem.

但是我该如何美白呢?我尝试将特征向量除以特征值:

But how do I perform whitening? I tried dividing the eigenvectors by the eigenvalues:

S, V = numpy.linalg.eig(cov)
V = V / S[:, numpy.newaxis]

，并使用V来转换数据，但这导致了奇怪的数据值. 有人可以切丝一点吗?

and used V to transform the data but this led to weird data values. Could someone please shred some light on this?

推荐答案

这是我从您还可以使用SVD增白矩阵:

You can also whiten a matrix using SVD:

def svd_whiten(X):

    U, s, Vt = np.linalg.svd(X, full_matrices=False)

    # U and Vt are the singular matrices, and s contains the singular values.
    # Since the rows of both U and Vt are orthonormal vectors, then U * Vt
    # will be white
    X_white = np.dot(U, Vt)

    return X_white

第二种方法稍慢一些，但数值上可能更稳定.

The second way is a bit slower, but probably more numerically stable.

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