Robust nonnegative matrix factorization via half-quadratic minimization

Abstract—Nonnegative matrix factorization (NMF) is a pop-ular technique for learning parts-based representation and data clustering. It usually uses the squared residuals to quantify the quality of factorization, which is optimal specifically to zero-mean, Gaussian noise and sensitive to outliers in general cases. In this paper, we propose a robust NMF method based on the correntropy induced metric, which is much more insensitive to outliers. A half-quadratic optimization algorithm is developed to solve the proposed problem efficiently. The proposed method is further extended to handle outlier rows by incorporating structural knowledge about the outliers. Experimental results on data sets with and without apparent outliers demonstrate the effectiveness of the proposed algorithms. Keywords-robust non-negative matrix factorization, half-quadratic optimization, correntropy induced metric I