Variational inference for nonparametric subspace dictionary learning with hierarchical beta process

Abstract

Nonparametric Bayesian models have been implemented in dictionary learning. However, for signal samples from multiple subspaces, existing methods only learn one uniform dictionary and thus are not optimal for representing the subspace structures. To address this issue, we first utilize a combination of Dirichlet process and hierarchical Beta process as priors to infer the latent subspace number and dictionary dimension automatically; second, to derive tractable variational inference, we modify the priors with the Sethuraman's construction and further employ the multinomial approximation. Experimental results indicate that our approach can achieve a set of nonparametric subspace dictionaries, while showing performance enhancements in the tasks of image denoising.