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 language | English (US) |
|---|---|
| Pages (from-to) | 1579-1601 |
| Number of pages | 23 |
| Journal | The Annals of Applied Statistics |
| Volume | 4 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2010 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Supported in part by Grants from the National Science Foundation (DMS-06-06580, DMS-09-07170), the National Cancer Institute (CA57030), the Virtual Center for Collaboration between Statisticians in the US and China, and King Abdullah University of Science and Technology (KAUST, Award KUS-CI-016-04).Supported in part by Grants from the National Science Foundation (DMS-07-06818) and the National Institute of Health (R01-RGM080503A, R21-CA129671).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.