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 t
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