Tensor-Factor Analysis

A nonparametric factor analysis framework is developed for tensor-variate data. The dictionary elements (factor loadings) are inferred as tensors, as opposed to vectors. Our tensor-factor analysis (TFA) framework is developed in the context of the beta-process factor analysis (BPFA) using a nonparametric tensor decomposition for each dictionary element. We extend the multiplicative gamma prior to allow inference of the shape parameter, which can help control model complexity during learning. Moreover, we extend the TFA model to include translation invariance and a multi-layer structure—a deep convolutional TFA. We test our approach on 2D & 3D image denoising, inpainting, and image classification. Our TFA models provide more diverse dictionaries. In particular, TFA provides state of the art results for simultaneous image inpainting & denoising and on the Caltech 101 benchmark.