Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture

TL;DR

This paper introduces a fast, hard clustering algorithm for evolving batch-sequential data based on the dependent Dirichlet process mixture model, offering convergence guarantees and improved accuracy over existing methods.

Contribution

It derives a low-variance asymptotic algorithm from the DDPMM, enabling efficient and accurate clustering of dynamic data with unknown cluster counts.

Findings

Requires significantly less computational time than existing algorithms.

Achieves higher clustering accuracy on synthetic and real data.

Provides convergence guarantees similar to k-means.

Abstract

This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computational time than contemporary probabilistic and hard clustering algorithms, while providing higher accuracy on the examined datasets.