Detecting the Dimensionality for Principal Components Model

Abstract

A crucial issue for principal components analysis (PCA) is to determine the number of principal components to capture the variability of usually high-dimensional data. In this article the dimension detection for PCA is formulated as a variable selection problem for regressions. The adaptive LASSO is used for the variable selection in this application. Simulations demonstrate that this approach is more accurate than existing methods in some cases and competitive in some others. The performance of this model is also illustrated using a real example.

Keywords:

• Adaptive LASSO
• Dimension reduction
• ECM algorithm
• Probabilistic PCA
• Singular value decomposition

Mathematics Subject Classification:

• 62H25
• 62J07

Acknowledgment

The authors thank the editor, associate editor, and anonymous referee for detailed comments that helped to improve the presentation of the article.