Cross-Validatory Choice of the Number of Components From a Principal Component Analysis

Abstract

A method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction. The correspondence between principal component analysis and the singular value decomposition of the data matrix is used. The method is based on successively predicting each element in the data matrix after deleting the corresponding row and column of the matrix, and makes use of recently published algorithms for updating a singular value decomposition. These are very fast, which renders the proposed technique a practicable one for routine data analysis.

KEY WORDS:

• Cross-validation
• Principal component analysis
• Reduction of dimensionality
• Singular value decomposition