A robust dimensionality reduction and matrix factorization framework for data clustering

Most existing Non-negative Matrix Factorization (NMF) related data clustering techniques directly decompose the original feature space while have not well considered the fact that the low dimensional feature space is always embedded in the high dimensional feature space and can better reveal the spatial distribution of data. In this letter, we propose a new matrix factorization model, which unites the objectives of clustering and dimensionality reduction simultaneously. In the proposed framework, the clustering based on matrix factorization is actually executed on the embedded subspace which may provide more accurate and reasonable solutions. Furthermore, we use the l(2,1)-norm instead of the conventional l(2)-norm to enhance the clustering results and make the clustering framework more robust to the noises and outliers. Meanwhile, in order to preserve as much as possible local similarity of the data, we have also employed an affinity matrix with special learning to introduce the manifold learning into the cluster indicator matrix. An optimization procedure based on Augmented Lagrangian Method (ALM) is devised to effectively solve the proposed problem and explicitly show the clustering results. Experimental results on the benchmark datasets with different proprieties exhibit the superior performance of the proposed method. (C) 2019 Published by Elsevier B.V.