Topic models with power-law using Pitman-Yor process

Abstract

One important approach for knowledge discovery and data mining is to estimate unobserved variables because latent variables can indicate hidden specific properties of observed data. The latent factor model assumes that each item in a record has a latent factor; the co-occurrence of items can then be modeled by latent factors. In document modeling, a record indicates a document represented as a "bag of words," meaning that the order of words is ignored, an item indicates a word and a latent factor indicates a topic. Latent Dirichlet allocation (LDA) is a widely used Bayesian topic model applying the Dirichlet distribution over the latent topic distribution of a document having multiple topics. LDA assumes that latent topics, i.e., discrete latent variables, are distributed according to a multinomial distribution whose parameters are generated from the Dirichlet distribution. LDA also models a word distribution by using a multinomial distribution whose parameters follows the Dirichlet distribution. This Dirichlet-multinomial setting, however, cannot capture the power-law phenomenon of a word distribution, which is known as Zipf's law in linguistics. We therefore propose a novel topic model using the Pitman-Yor(PY) process, called the PY topic model. The PY topic model captures two properties of a document; a power-law word distribution and the presence of multiple topics. In an experiment using real data, this model outperformed LDA in document modeling in terms of perplexity.