Bayesian Clustering of Shapes of Curves

TL;DR

This paper introduces a Bayesian clustering method for shape analysis of curves that automatically infers the number of clusters using an elastic shape metric and MCMC sampling, applicable to diverse scientific data.

Contribution

It develops a novel Bayesian approach utilizing an elastic shape metric and Wishart modeling, enabling automatic inference of cluster numbers in curve shape data.

Findings

Effective on synthetic and real datasets

Automatically determines the number of clusters

Applicable to protein, cell, and image shape data

Abstract

Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an efficient Bayesian method to cluster curve data using an elastic shape metric that is based on joint registration and comparison of shapes of curves. The elastic-inner product matrix obtained from the data is modeled using a Wishart distribution whose parameters are assigned carefully chosen prior distributions to allow for automatic inference on the number of clusters. Posterior is sampled through an efficient Markov chain Monte Carlo procedure based on the Chinese restaurant process to infer (1) the posterior distribution on the number of clusters, and (2) clustering configuration of shapes. This method is demonstrated on a variety of synthetic data and real data examples on protein structure analysis, cell shape analysis in microscopy images, and clustering of shaped from MPEG7 database.