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Activity Number: 332 - SPEED: Section on Bayesian Statistical Science
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #324883 View Presentation
Title: Bayesian Clustering on Stiefel Manifolds
Author(s): Ritendranath Mitra* and Subhajit Sengupta and Subhadip Pal
Companies: and NorthShore University Health System and University of Louisville
Keywords: Stiefel ; conjugacy ; slice sampling ; Metropolis Hastings ; clustering ; normalizing constant.
Abstract:

Complex data objects, like images and diffusion tensors, lie on non-Euclidean spaces, like manifolds. We propose a novel posterior inference scheme to cluster data embedded in a Steifel manifold. It is centered around a non-parametric Bayesian prior to accomodate random number of clusters. A key challenge is a complexity of some posterior conditionals involving intractable normalizing constants. To handle this, we borrowed asymptotic results from frequentist literature for good initialization schemes, and suitable approximations of the normalizing constant. Additionally, using tail properties of these densities and formally establishing their unimodality, we came up with an efficient proposal scheme. These techniques were finally integrated into an efficient slice sampling scheme. Synthetic data validated the power of the algorithm and its robustness to diverse parameter settings. A motivating data example is provided.


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