Abstract
Nonnegative matrix factorization (NMF) is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF (SNMF) and weighted NMF (WNMF) can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative decomposition (RMND), is proposed to discover the latent clustering structure from the pairwise similarity matrix. The RMND model is derived from the nonlinear NMF algorithm. RMND decomposes a pairwise similarity matrix into a product of three low rank nonnegative matrices. The pairwise similarity matrix is represented as a transformation of a positive semidefinite matrix which pops out the latent clustering structure. We develop a learning procedure based on multiplicative update rules and steepest descent method to calculate the nonnegative solution of RMND. Experimental results in four different databases show that the proposed RMND approach achieves higher clustering accuracy.
Highlights
Nonnegative matrix factorization NMF 1 has been introduced as an effective technique for analyzing the latent structure of nonnegative data such as images and documents
The overall cost of Symmetric NMF (SNMF), Weighted NMF (WNMF), and Relationship Matrix Nonnegative Decomposition (RMND) is related to qn[2], where n is the number of samples
We have presented a novel relationship matrix nonnegative decomposition RMND model for data clustering task
Summary
Nonnegative matrix factorization NMF 1 has been introduced as an effective technique for analyzing the latent structure of nonnegative data such as images and documents. Symmetric NMF SNMF 10 is an extension of NMF It aims at learning clustering structure from the kernel matrix or pairwise similarity matrix which is positive semidefinite. When the similarity matrix is not positive semidefinite, SNMF is not able to capture the clustering structure. In SNMF, WNMF, and SSNMF, the low rank approximation to the pairwise similarity matrix is used. It is more sensitive to the unexpected noise It may produce undesirable performances in clustering tasks by minimizing the objective function from the viewpoint of reconstruction in the form as SNMF, WNMF, and SSNMF. We present a novel model, called relationship matrix nonnegative decomposition RMND , for data clustering tasks. According to the positive semidefiniteness, the SNMF formulation is incorporated in RMND, and a more tractable representation of pairwise similarity matrix is obtained. The detailed update rules for A and S can be found in 10
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