A Generalization of Principal Components Analysis to the Exponential Family

Abstract

Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponen-tial family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss func-tions, and give examples on simulated data. 1