Robust Asymmetric Bayesian Adaptive Matrix Factorization

Low rank matrix factorizations(LRMF) have attracted much attention due to its wide range of applications in computer vision, such as image impainting and video denoising. Most of the existing methods assume that the loss between an observed measurement matrix and its bilinear factorization follows symmetric distribution, like gaussian or gamma families. However, in real-world situations, this assumption is often found too idealized, because pictures under various illumination and angles may suffer from multi-peaks, asymmetric and irregular noises. To address these problems, this paper assumes that the loss follows a mixture of Asymmetric Laplace distributions and proposes robust Asymmetric Laplace Adaptive Matrix Factorization model(ALAMF) under bayesian matrix factorization framework. The assumption of Laplace distribution makes our model more robust and the asymmetric attribute makes our model more flexible and adaptable to real-world noise. A variational method is then devised for model inference. We compare ALAMF with other state-of-the-art matrix factorization methods both on data sets ranging from synthetic and real-world application. The experimental results demonstrate the effectiveness of our proposed approach.