Robust manifold matrix factorization for joint clustering and feature extraction

Low-rank matrix approximation has been widely used for data subspace clustering and feature representation in many computer vision and pattern recognition applications. However, in order to enhance the discriminability, most of the matrix approximation based feature extraction algorithms usually generate the cluster labels by certain clustering algorithm (e.g., the kmeans) and then perform the matrix approximation guided by such label information. In addition, the noises and outliers in the dataset with large reconstruction errors will easily dominate the objective function by the conventional ℓ2-norm based squared residue minimization. In this paper, we propose a novel clustering and feature extraction algorithm based on an unified low-rank matrix factorization framework, which suggests that the observed data matrix can be approximated by the production of projection matrix and low dimensional representation, among which the low-dimensional representation can be approximated by the cluster indicator and latent feature matrix simultaneously. Furthermore, we have proposed using the ℓ2,1-norm and integrating the manifold regularization to further promote the proposed model. A novel Augmented Lagrangian Method (ALM) based procedure is designed to effectively and efficiently seek the optimal solution of the problem. The experimental results in both clustering and feature extraction perspectives demonstrate the superior performance of the proposed method.