Existing nonnegative matrix factorization methods usually focus on learning global structure of the data to construct basis and coefficient matrices, which ignores local that commonly exists among data. To overcome this drawback, in paper, we propose a new type method, learns similarity clustering mutually enhanced way. The learned representation is more representative it better reveals inheren...

Learning fruitful representation from data is one of fundamental problems in machine learning and pattern recognition. Various methods have been developed, including factor analysis, principal component analysis (PCA), independent component analysis (ICA), manifold learning, and so on. Among those, nonnegative matrix factorization (NMF) has recently drawn extensive attention, since promising re...

We show that there exist real numbers λ1, λ2, . . . , λn that occur as the eigenvalues of an entry-wise nonnegative n-by-n matrix but do not occur as the eigenvalues of a symmetric nonnegative n-by-n matrix. This solves a problem posed by Boyle and Handelman, Hershkowitz, and others. In the process, recent work by Boyle and Handelman that solves the nonnegative inverse eigenvalue problem by app...

Nonnegative Matrix Factorization (NMF) can be used to approximate a large nonnegative matrix as a product of two smaller nonnegative matrices. This paper shows in detail how an NMF algorithm based on Newton iteration can be derived utilizing the general Karush-KuhnTucker (KKT) conditions for first-order optimality. This algorithm is suited for parallel execution on shared-memory systems. It was...