2021.10.27 8:40 N625

Matrix decomposition is a popular and fundamental approach in machine learning. The classical matrix decomposition methods with Frobenius norm loss is only optimal for Gaussian noise and thus suffer from the sensitivity to outliers and non-Gaussian noise. To address these limitations, the proposed methods can be divided into two categories. One type of approach is to replace the Frobenius norm loss with robust loss functions. The other type of approach is to impose the Bayesian priors to reduce the risk of overfitting. This paper combines these two approaches. Specifically, we model the noise by a mixture of Gaussian distribution, enabling the model to approximate a wide range of noise distributions. Meanwhile, we put a Laplace prior on the basis matrix to enforce the sparsity and a Dirichlet prior on the coefficient matrix to improve the interpretability. Extensive experiments in synthetic data and real-world data demonstrate that this method outperforms several competing ones. Ablation studies show that this method benefits from both the Bayesian priors and the Mixture of Gaussian noise loss, which confirms the necessity of combining the two schemes.