Abstract:
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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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