Low-rank Matrix Factorization under General Mixture Noise Distributions

Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problems using L1-norm and L2-norm losses, which mainly deal with Laplacian and Gaussian noises, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP (PMoEP) model by combining the penalized likelihood method with MoEP distributions. Such setting facilitates the learned LRMF model capable of automatically fitting the real noise through MoEP distributions. Each component in this mixture is adapted from a series of preliminary super- or sub-Gaussian candidates. Moreover, by facilitating the local continuity of noise components, we embed Markov random field into the PMoEP model and further propose the advanced PMoEP-MRF model. An Expectation Maximization (EM) algorithm and a variational EM (VEM) algorithm are also designed to infer the parameters involved in the proposed PMoEP and the PMoEP-MRF model, respectively. The superseniority of our methods is demonstrated by extensive experiments on synthetic data, face modeling, hyperspectral image restoration and background subtraction.