A Combinatorial View of Graph Laplacians

Huang, J

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A Combinatorial View of Graph Laplacians

Huang, J.(2005). A Combinatorial View of Graph Laplacians (144). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D499-0 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-8809-B

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MPIK-TR-144.pdf (Publisher version), 204KB

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Huang, J^{1, 2}, Author

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1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794

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Abstract: Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence for the normalized Laplacian. In this paper, we analyze different variants of graph Laplacians directly from the ways solving the original graph partitioning problem. The graph partitioning problem is a well-known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.

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Dates: Published in Print: 2005-08

Publication Status: Published in print

Pages: 9

Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics

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Identifiers: Report Nr.: 144
BibTex Citekey: 3534

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Title: Technical Report of the Max Planck Institute for Biological Cybernetics

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Pages: - Volume / Issue: 144 Sequence Number: - Start / End Page: - Identifier: -