Title: A General Model for Robust Tensor Factorization with Unknown Noise,
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.