Discrete PCA

Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic indexing, genotype inference with admixture, non-negative matrix factorization, latent Dirichlet allocation, multinomial PCA, and Gamma-Poisson models. Statistical methodologies for developing algorithms are equally as varied, although this talk will focus on the Bayesian framework. The most well published application is genetype inference, but text analysis is now increasingly seeing use because the algorithms cope with very large sparse matrices. This talk will present the general model, a discrete version of both PCA and ICA, present alternative representations, and several algorithms (mean field and Gibbs).