Cross-validation of component models: A critical look at current methods
- 24 January 2008
- journal article
- review article
- Published by Springer Science and Business Media LLC in Analytical and Bioanalytical Chemistry
- Vol. 390 (5), 1241-1251
- https://doi.org/10.1007/s00216-007-1790-1
Abstract
In regression, cross-validation is an effective and popular approach that is used to decide, for example, the number of underlying features, and to estimate the average prediction error. The basic principle of cross-validation is to leave out part of the data, build a model, and then predict the left-out samples. While such an approach can also be envisioned for component models such as principal component analysis (PCA), most current implementations do not comply with the essential requirement that the predictions should be independent of the entity being predicted. Further, these methods have not been properly reviewed in the literature. In this paper, we review the most commonly used generic PCA cross-validation schemes and assess how well they work in various scenarios.Keywords
This publication has 12 references indexed in Scilit:
- Cross-validation of multiway component modelsJournal of Chemometrics, 1999
- Weighted least squares fitting using ordinary least squares algorithmsPsychometrika, 1997
- Selection of optimal regression models via cross‐validationJournal of Chemometrics, 1988
- Cross-validatory choice in principal component analysis; some sampling resultsJournal of Statistical Computation and Simulation, 1983
- Cross-Validatory Choice of the Number of Components From a Principal Component AnalysisTechnometrics, 1982
- Cross-Validatory Estimation of the Number of Components in Factor and Principal Components ModelsTechnometrics, 1978
- Pattern recognition by means of disjoint principal components modelsPattern Recognition, 1976
- A predictive approach to the random effect modelBiometrika, 1974
- The Relationship Between Variable Selection and Data Agumentation and a Method for PredictionTechnometrics, 1974
- I. Problems and Designs of Cross-Validation 1Educational and Psychological Measurement, 1951