Abstract

We investigate a generalized linear model for dimensionality reduction of binary data. The model is related to principal component analysis (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 coe#cients of the logistic PCA model. The resulting updates have a simple closed form and are guaranteed at each iteration to improve the model's likelihood. We evaluate the performance of logistic PCA---as measured by reconstruction error rates---on data sets drawn from four real world applications.

Citations