Selecting the number of components in principal component analysis using cross-validation approximations
Selecting the number of components in principal component analysis using cross-validation approximations
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DOI：
10.1016/j.csda.2011.11.012
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发表时间：
2012-06-01
影响因子：
1.8
通讯作者：
Husson, Francois
中科院分区：
文献类型：
--
作者：
Josse, Julie;Husson, Francois
交叉验证是主成分分析（PCA）中选择成分数量的一种久经考验的方法，然而，其主要缺点是计算成本。在回归（或非参数回归）设置中，诸如通用交叉验证（GCV）之类的标准提供了方便的近似，以进行留一交叉验证。它们是基于预测误差和由投影矩阵（或平滑矩阵）的元素加权的残差平方和之间的关系。然后，使用具有唯一投影矩阵的PCA的原始表示在PCA中建立这样的关系。它允许定义两个交叉验证近似准则：交叉验证准则的平滑近似（SACV）和GCV准则。该方法进行了评估与模拟，并给出了有前途的结果。皇冠版权所有（c）2011由爱思唯尔B.V.出版保留所有权利。
Cross-validation is a tried and tested approach to select the number of components in principal component analysis (PCA), however, its main drawback is its computational cost. In a regression (or in a non parametric regression) setting, criteria such as the general cross-validation one (GCV) provide convenient approximations to leave-one-out cross-validation. They are based on the relation between the prediction error and the residual sum of squares weighted by elements of a projection matrix (or a smoothing matrix). Such a relation is then established in PCA using an original presentation of PCA with a unique projection matrix. It enables the definition of two cross-validation approximation criteria: the smoothing approximation of the cross-validation criterion (SACV) and the GCV criterion. The method is assessed with simulations and gives promising results. Crown Copyright (c) 2011 Published by Elsevier B.V. All rights reserved.