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On the use of the observation‐wise k ‐fold operation in PCA cross‐validation
Author(s) -
Saccenti Edoardo,
Camacho José
Publication year - 2015
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2726
Subject(s) - cross validation , fold (higher order function) , principal component analysis , algorithm , computer science , independence (probability theory) , set (abstract data type) , mathematics , artificial intelligence , statistics , programming language
Cross‐validation (CV) is a common approach for determining the optimal number of components in a principal component analysis model. To guarantee the independence between model testing and calibration, the observation‐wise k ‐fold operation is commonly implemented in each cross‐validation step. This operation renders the CV algorithm computationally intensive, and it is the main limitation to apply CV on very large data sets. In this paper, we carry out an empirical and theoretical investigation of the use of this operation in the element‐wise k ‐fold ( ekf ) algorithm, the state‐of‐the‐art CV algorithm. We show that when very large data sets need to be cross‐validated and the computational time is a matter of concern, the observation‐wise k ‐fold operation can be skipped. The theoretical properties of the resulting modified algorithm, referred to as column‐wise k ‐fold ( ckf ) algorithm, are derived. Also, its performance is evaluated with several artificial and real data sets. We suggest the ckf algorithm to be a valid alternative to the standard ekf to reduce the computational time needed to cross‐validate a data set. Copyright © 2015 John Wiley & Sons, Ltd.