Direct Robust Matrix Factorizatoin for Anomaly Detection

Matrix factorization methods are extremely useful in many data mining tasks, yet their performances are often degraded by outliers. In this paper, we propose a novel robust matrix factorization algorithm that is insensitive to outliers. We directly formulate robust factorization as a matrix approximation problem with constraints on the rank of the matrix and the cardinality of the outlier set. Then, unlike existing methods that resort to convex relaxations, we solve this problem directly and efficiently. In addition, structural knowledge about the outliers can be incorporated to find outliers more effectively. We applied this method in anomaly detection tasks on various data sets. Empirical results show that this new algorithm is effective in robust modeling and anomaly detection, and our direct solution achieves superior performance over the state-of-the-art methods based on the L1-norm and the nuclear norm of matrices.