scholarly journals Nonnegative Matrix Factorization for Combinatorial Optimization: Spectral Clustering, Graph Matching, and Clique Finding

2008 ◽  
Author(s):  
Chris Ding ◽  
Tao Li ◽  
Michael I. Jordan
Keyword(s):  
Combinatorial Optimization ◽  
Matrix Factorization ◽  
Spectral Clustering ◽  
Nonnegative Matrix Factorization ◽  
Graph Matching ◽  
Nonnegative Matrix

scholarly journals Image Retrieval Based on Multiview Constrained Nonnegative Matrix Factorization and Gaussian Mixture Model Spectral Clustering Method

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Qunyi Xie ◽  
Hongqing Zhu
Keyword(s):  
Image Retrieval ◽  
Objective Function ◽  
Matrix Factorization ◽  
Spectral Clustering ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Gaussian Mixture ◽  
Sparse Representations ◽  
Clustering Method ◽  
Spectral Clustering Method

Content-based image retrieval has recently become an important research topic and has been widely used for managing images from repertories. In this article, we address an efficient technique, called MNGS, which integrates multiview constrained nonnegative matrix factorization (NMF) and Gaussian mixture model- (GMM-) based spectral clustering for image retrieval. In the proposed methodology, the multiview NMF scheme provides competitive sparse representations of underlying images through decomposition of a similarity-preserving matrix that is formed by fusing multiple features from different visual aspects. In particular, the proposed method merges manifold constraints into the standard NMF objective function to impose an orthogonality constraint on the basis matrix and satisfy the structure preservation requirement of the coefficient matrix. To manipulate the clustering method on sparse representations, this paper has developed a GMM-based spectral clustering method in which the Gaussian components are regrouped in spectral space, which significantly improves the retrieval effectiveness. In this way, image retrieval of the whole database translates to a nearest-neighbour search in the cluster containing the query image. Simultaneously, this study investigates the proof of convergence of the objective function and the analysis of the computational complexity. Experimental results on three standard image datasets reveal the advantages that can be achieved with the proposed retrieval scheme.

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