Applying Discrete PCA in Data Analysis
This work provides incremental improvements to existing methods for discrete data analysis, potentially benefiting researchers in fields like text mining and statistics.
The paper explores extensions to principal component analysis for discrete data, interpreting them as a discrete version of independent component analysis and developing hierarchical and Gibbs sampling techniques, with applications in text prediction and information retrieval.
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 analysis, and genotype inference with admixture. In this paper we explore a number of extensions to the common theory, and present some application of these methods to some common statistical tasks. We show that these methods can be interpreted as a discrete version of ICA. We develop a hierarchical version yielding components at different levels of detail, and additional techniques for Gibbs sampling. We compare the algorithms on a text prediction task using support vector machines, and to information retrieval.