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

Nonnegative matrix factorization (NMF) is a versatile model for data clustering. In this paper, we propose several NMF inspired algorithms to solve different data mining problems. They include (1) multi-way normalized cut spectral clustering, (2) graph matching of both undirected and directed graphs...

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Bibliographic Details
Published in2008 Eighth IEEE International Conference on Data Mining pp. 183 - 192
Main Authors Ding, C., Tao Li, Jordan, M.I.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2008
Subjects
clique finding
clustering
Clustering algorithms
Cost function
Data analysis
Data mining
DH-HEMTs
graph matching
Lagrangian functions
Linear discriminant analysis
Nonnegative matrix factorization
Support vector machine classification
Support vector machines
Unsupervised learning
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Summary:Nonnegative matrix factorization (NMF) is a versatile model for data clustering. In this paper, we propose several NMF inspired algorithms to solve different data mining problems. They include (1) multi-way normalized cut spectral clustering, (2) graph matching of both undirected and directed graphs, and (3) maximal clique finding on both graphs and bipartite graphs. Key features of these algorithms are (a) they are extremely simple to implement; and (b) they are provably convergent. We conduct experiments to demonstrate the effectiveness of these new algorithms. We also derive a new spectral bound for the size of maximal edge bicliques as a byproduct of our approach.
ISBN:076953502X
9780769535029
ISSN:1550-4786
2374-8486
DOI:10.1109/ICDM.2008.130