Learning a Subspace and Clustering Simultaneously with Manifold Regularized Nonnegative Matrix Factorization

With the incredible growth of high-dimensional data such as microarray gene expression data and web blogs from internet, the researchers are desirable to develop new clustering techniques to address the critical problem created by irrelevant dimensions. Properties of Nonnegative Matrix Factorization (NMF) as a clustering method were studied by relating its formulation to other methods such as K-means clustering. In this paper, by introducing clustering indicator constraints on NMF and incorporating manifold regularization to preserve geometric structures, we propose a novel manifold regularized NMF method that can simultaneously learn subspace and do clustering. As a result, our clustering results can directly assign cluster label to data points. Extensive experimental results show that our method outperforms related other methods.