Feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering

Abstract Non-negative matrix factorization (NMF) can map high-dimensional data into a low-dimensional data space. Feature selection can eliminate the redundant and irrelevant features from the alternative features. In this paper, we propose a feature selection based dual-graph sparse non-negative matrix factorization (DSNMF) which can find an appropriate low dimensional representation of data by NMF and then select more discriminative features to further reduce the dimension of the low dimensional space by feature selection rather than reduce the dimension by only NMF or feature selection in many previous methods. DSNMF combines dual-graph model with non-negative matrix factorization, which can not only simultaneously preserve the geometric structures in both the data space and the feature space, but also make the two non-negative matrix factors update iteratively and interactively. In addition, DSNMF exerts L2,1-norm constraint on the non-negative matrix factor of the feature space to make full use of the sparse self-representation information. What's more, we propose a new local discriminative feature selection clustering called feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering (DSNMF-LDC) whose clustering effects are better. We give the objective function, the iterative updating rules and the convergence proof. Our empirical study shows that DSNMF-LDC is robust and excellent in comparison to 9 feature selection algorithms and 7 clustering algorithms in clustering accuracy (ACC) and normalized mutual information (NMI).