Bayesian Rose Trees

TL;DR

This paper introduces a Bayesian hierarchical clustering method that constructs rose trees with arbitrary branching, improving over traditional binary-only hierarchies by better modeling data structures.

Contribution

It presents a novel Bayesian algorithm for constructing rose trees with arbitrary branching, enhancing flexibility over binary hierarchical clustering methods.

Findings

Rose trees better model data than binary hierarchies.

The greedy algorithm efficiently finds high-likelihood rose trees.

Experiments demonstrate improved data representation with rose trees.

Abstract

Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while computationally convenient, is often undesirable. In this paper we explore a Bayesian hierarchical clustering algorithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy agglomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.