PCA에서 최적 PC 개수를 정하기 위한 Cross-validation 방법

1. Row-wise cross-validation $$\begin{aligned} CV(k) &= \sum_{i=1}^N \lvert \lvert \mathbf{x}_i - \boldsymbol{\xi} \boldsymbol{f}i^T \lvert\vert^2 \ &= \sum{i=1}^N \lvert \lvert \mathbf{x}_i - \boldsymbol{\xi} (\mathbf{x}_i^T\boldsymbol{\xi})^T \lvert\vert^2 \end{aligned}$$ where $\boldsymbol\xi$ is a PC function(PC loading) with $k$ eigenvectors and $\boldsymbol{f}_i$ is $i$th PC score with $k$ components. $\mathbf{x}_i$를 predict하는

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