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Because of the limitations of matrix factorization, such as losing spatialstructure information, the concept of low-rank tensor factorization (LRTF) hasbeen applied for the recovery of a low dimensional subspace from highdimensional visual data. The low-rank tensor recovery is generally achieved byminimizing the loss function between the observed data and the factorizationrepresentation. The loss function is designed in various forms under differentnoise distribution assumptions, like $L_1$ norm for Laplacian distribution and$L_2$ norm for Gaussian distribution. However, they often fail to tackle thereal data which are corrupted by the noise with unknown distribution. In thispaper, we propose a generalized weighted low-rank tensor factorization method(GWLRTF) integrated with the idea of noise modelling. This procedure treats thetarget data as high-order tensor directly and models the noise by a Mixture ofGaussians, which is called MoG GWLRTF. The parameters in the model areestimated under the EM framework and through a new developed algorithm ofweighted low-rank tensor factorization. We provide two versions of thealgorithm with different tensor factorization operations, i.e., CPfactorization and Tucker factorization. Extensive experiments indicate therespective advantages of this two versions in different applications and alsodemonstrate the effectiveness of MoG GWLRTF compared with other competingmethods.

A General Model for Robust Tensor Factorization with Unknown Noise