Logistic PCA Through an Extension of Pearson's MSE Optimality Criterion to Binary Data

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Andrew Landgraf*+ and Yoonkyung Lee
• Companies: Ohio State University and Ohio State University
• Keywords: Binary data ; Dimension reduction ; Logistic PCA ; PCA

Abstract

Principal component analysis (PCA) for binary data, known as logistic PCA, has been studied several times over the last fifteen years, all of which extend the singular value decomposition motivation of ordinary PCA. We propose a new formulation of logistic PCA which extends Pearson's MSE optimality motivation for PCA to binary data. Our formulation does not require solving a matrix factorization, as previous methods do, but instead looks for projections of the saturated natural parameters. We provide computationally efficient methods of solving for the principal component loadings, one of which finds a globally optimal solution over a convex relaxation of low rank projection matrices. We apply our logistic PCA to a medical diagnoses data set from OSU's intensive care unit in order to characterize the co-morbidity as latent factors, which can be used to define patient profiles for prediction of other clinical outcomes.