Optimal Whitening and Decorrelation
Optimal Whitening and Decorrelation
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DOI：
10.1080/00031305.2016.1277159
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发表时间：
2018-01-01
影响因子：
1.8
通讯作者：
Strimmer, Korbinian
中科院分区：
文献类型：
--
作者：
Kessy, Agnan;Lewin, Alex;Strimmer, Korbinian
白化或球形化是统计分析中将随机变量转换为正交性的常见预处理步骤。然而，由于旋转自由度，存在无限多种可能的美白程序。因此，使用了多种球形方法，例如基于主成分分析 (PCA)、Cholesky 矩阵分解和零相位成分分析 (ZCA) 等。在这里，我们概述了基本理论并讨论了五种自然美白程序。随后，我们证明，研究球体变量和原始变量之间的互协方差和互相关矩阵可以打破旋转不变性并识别最佳白化变换。因此，我们推荐两种特定的方法：ZCA-cor 白化以产生与原始变量最大程度相似的球形变量，以及 PCA-cor 白化以获取最大限度地压缩原始变量的球形变量。
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example, based on principal component analysis (PCA), Cholesky matrix decomposition, and zero-phase component analysis (ZCA), among others. Here, we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables.