A Generalized Linear Model for Principal Component Analysis of Binary Data

Abstract

VVe investigate a generalized linear model fbr dimensionality reduction of binary data. The model is related to principal component anal- ysis (PCA) in the same way that logistic regression is related to linear regression. Thus we refer to the model as logistic PCA. In this paper, we derive an alternating least squares method to estimate the basis vectors and generalized linear coefficients of the logistic PCA model. The resulting updates have a simple closed ibrm and are guaranteed at each iteration to improve the model's likelihood. We evaluate the perfbrmance of logistic PCA as measured by reconstruction error rates on data sets drawn from four real world applications.