Towards Robust Co-Clustering

Nonnegative Matrix Tri-factorization (NMTF) and its graph regularized extensions have been widely used for co-clustering task to group data points and features simultaneously. However existing methods are sensitive to noises and outliers which is because of the squared loss function is used to measure the quality of data reconstruction and graph regularization. In this paper, we extend GNMTF by introducing a sparse outlier matrix into the data reconstruction function and applying the `1 norm to measure graph dual regularization errors, which leads to a novel Robust Co-Clustering (RCC) method. Accordingly, RCC is expected to obtain a more faithful approximation to the data recovered from sparse outliers, and achieve robust regularization by reducing the regularization errors of unreliable graphs via `1 norm. To solve the optimization problem of RCC, an alternating iterative algorithm is provided and its convergence is also proved. We also show the connection between the sparse outlier matrix in data reconstruction function and the robust Huber M-estimator. Experimental results on real-world data sets show that our RCC consistently outperforms the other algorithms in terms of clustering performance, which validates the effectiveness and robustness of the proposed approach.