Sparse logistic principal components analysis for binary data

Seokho Lee, Jianhua Z. Huang, Jianhua Hu

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

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. © Institute ol Mathematical Statistics, 2010.
Original languageEnglish (US)
Pages (from-to)1579-1601
Number of pages23
JournalThe Annals of Applied Statistics
Volume4
Issue number3
DOIs
StatePublished - Sep 2010
Externally publishedYes

Fingerprint

Dive into the research topics of 'Sparse logistic principal components analysis for binary data'. Together they form a unique fingerprint.

Cite this