Summary Statistics for Partitionings and Feature Allocations
This work addresses the challenge of interpreting complex clustering results for researchers using Bayesian nonparametric models, though it appears incremental as it builds on existing methods for summarizing partitionings.
The paper tackles the problem of interpreting diffuse posterior samples from infinite mixture models by introducing novel statistics based on block sizes to represent partitionings and feature allocations, and proposes an entropy agglomeration algorithm for summarization and visualization, with experiments showing practical utility.
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.