Bayesian Clustering of Shapes of Curves
This addresses the need for shape-based clustering in scientific domains like biology and image analysis, offering an incremental improvement over existing model-based techniques.
The paper tackles the problem of unsupervised clustering of curves by shape, developing a Bayesian method that uses an elastic shape metric and Wishart distribution modeling to automatically infer the number of clusters, with applications in protein structure, cell shape, and MPEG7 database analysis.
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.