A General Model for Robust Tensor Factorization with Unknown Noise

TL;DR

This paper introduces a robust tensor factorization model that effectively handles unknown noise distributions in high-dimensional data by modeling noise with a Mixture of Gaussians and employing EM-based parameter estimation.

Contribution

It proposes a generalized weighted low-rank tensor factorization method incorporating noise modeling with Mixture of Gaussians, applicable with CP and Tucker tensor decompositions.

Findings

Outperforms existing methods in noise robustness.

Effective in various high-dimensional visual data applications.

Demonstrates advantages of two tensor factorization approaches.

Abstract

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional visual data. The low-rank tensor recovery is generally achieved by minimizing the loss function between the observed data and the factorization representation. The loss function is designed in various forms under different noise distribution assumptions, like $L_1$ norm for Laplacian distribution and $L_2$ norm for Gaussian distribution. However, they often fail to tackle the real data which are corrupted by the noise with unknown distribution. In this paper, we propose a generalized weighted low-rank tensor factorization method (GWLRTF) integrated with the idea of noise modelling. This procedure treats the target data as high-order tensor directly and models the noise by a Mixture of Gaussians, which is called MoG GWLRTF. The parameters in the model are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization. We provide two versions of the algorithm with different tensor factorization operations, i.e., CP factorization and Tucker factorization. Extensive experiments indicate the respective advantages of this two versions in different applications and also demonstrate the effectiveness of MoG GWLRTF compared with other competing methods.