The Annals of Applied Statistics

Sparse logistic principal components analysis for binary data

Seokho Lee, Jianhua Z. Huang, and Jianhua Hu

Full-text: Open access

Abstract

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success probabilities of the binary observations. Sparsity is introduced to the principal component (PC) loading vectors for enhanced interpretability and more stable extraction of the principal components. Our sparse PCA is formulated as solving an optimization problem with a criterion function motivated from a penalized Bernoulli likelihood. A Majorization–Minimization algorithm is developed to efficiently solve the optimization problem. The effectiveness of the proposed sparse logistic PCA method is illustrated by application to a single nucleotide polymorphism data set and a simulation study.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 3 (2010), 1579-1601.

Dates
First available in Project Euclid: 18 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1287409387

Digital Object Identifier
doi:10.1214/10-AOAS327

Mathematical Reviews number (MathSciNet)
MR2758342

Zentralblatt MATH identifier
1202.62084

Keywords
Binary data dimension reduction MM algorithm LASSO PCA regularization sparsity

Citation

Lee, Seokho; Huang, Jianhua Z.; Hu, Jianhua. Sparse logistic principal components analysis for binary data. Ann. Appl. Stat. 4 (2010), no. 3, 1579--1601. doi:10.1214/10-AOAS327. https://projecteuclid.org/euclid.aoas/1287409387


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Supplemental materials

  • Supplementary material: The MM algorithm for sparse logistic PCA using the tight bound. We develop the MM algorithm for sparse logistic PCA using the tight majorizing bound. Comparison of the developed algorithm with the MM algorithm using the uniform bound in terms of computing time is also presented.