Model-Based Hierarchical Clustering

TL;DR

This paper introduces a Bayesian model-based hierarchical clustering method that automatically determines the optimal cluster hierarchy, feature sharing, and model complexity, demonstrated on synthetic and real document data.

Contribution

It proposes a novel Bayesian framework for hierarchical clustering that jointly models feature distributions and automatically infers the hierarchy structure.

Findings

Automatically determines the number of clusters and hierarchy depth.

Effectively models feature sharing across clusters.

Performs well on synthetic and real document datasets.

Abstract

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that is a key component of our model. Features can have either a unique distribution in every cluster or a common distribution over some (or even all) of the clusters. The cluster subsets over which these features have such a common distribution correspond to the nodes (clusters) of the tree representing the hierarchy. We apply this general model to the problem of document clustering for which we use a multinomial likelihood function and Dirichlet priors. Our algorithm consists of a two-stage process wherein we first perform a flat clustering followed by a modified hierarchical agglomerative merging process that includes determining the features that will have common distributions over the merged clusters. The regularization induced by using the marginal likelihood automatically determines the optimal model structure including number of clusters, the depth of the tree and the subset of features to be modeled as having a common distribution at each node. We present experimental results on both synthetic data and a real document collection.