# Dirichlet-vMF Mixture Model

## TL;DR

This paper introduces VMFMix, a mixture model that captures co-occurrence patterns across documents using a continuous hypersphere, enabling the derivation of topic embeddings from multiple embedding sets.

## Contribution

The paper proposes VMFMix, a novel Dirichlet-vMF mixture model with an efficient inference algorithm for deriving topic embeddings on a hypersphere.

## Key findings

- VMFMix performs well on document classification tasks.
- The model effectively captures co-occurrence patterns across documents.
- Preliminary analysis shows promising results.

## Abstract

This document is about the multi-document Von-Mises-Fisher mixture model with a Dirichlet prior, referred to as VMFMix. VMFMix is analogous to Latent Dirichlet Allocation (LDA) in that they can capture the co-occurrence patterns acorss multiple documents. The difference is that in VMFMix, the topic-word distribution is defined on a continuous n-dimensional hypersphere. Hence VMFMix is used to derive topic embeddings, i.e., representative vectors, from multiple sets of embedding vectors. An efficient Variational Expectation-Maximization inference algorithm is derived. The performance of VMFMix on two document classification tasks is reported, with some preliminary analysis.