Robust Tensor Factorization with Unknown Noise

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of tensor factorization has been applied for the recovery of a low dimensional subspace from high dimensional visual data. Generally, the recovery is achieved by minimizing the loss function between the observed data and the factorization representation. Under different assumptions of the noise distribution, the loss functions are in various forms, like L-1 and L-2 norms. However, real data are often corrupted by noise with an unknown distribution. Then any specific form of loss function for one specific kind of noise often fails to tackle such real data with unknown noise. In this paper, we propose a tensor factorization algorithm to model the noise as a Mixture of Gaussians (MoG). As MoG has the ability of universally approximating any hybrids of continuous distributions, our algorithm can effectively recover the low dimensional subspace from various forms of noisy observations. The parameters of MoG are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization (WLRTF). The effectiveness of our algorithm are substantiated by extensive experiments on both of synthetic data and real image data.