Robust Capped Norm Nonnegative Matrix Factorization

As an important matrix factorization model, Nonnegative Matrix Factorization (NMF) has been widely used in information retrieval and data mining research. Standard Nonnegative Matrix Factorization is known to use the Frobenius norm to calculate the residual, making it sensitive to noises and outliers. It is desirable to use robust NMF models for practical applications, in which usually there are many data outliers. It has been studied that the 2,1, or 1-norm can be used for robust NMF formulations to deal with data outliers. However, these alternatives still suffer from the extreme data outliers. In this paper, we present a novel robust capped norm orthogonal Nonnegative Matrix Factorization model, which utilizes the capped norm for the objective to handle these extreme outliers. Meanwhile, we derive a new efficient optimization algorithm to solve the proposed non-convex non-smooth objective. Extensive experiments on both synthetic and real datasets show our proposed new robust NMF method consistently outperforms related approaches.