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A Combinatorial View of the Graph Laplacians (2005)
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BibTeX
@MISC{Huang05acombinatorial,
author = {Jiayuan Huang},
title = {A Combinatorial View of the Graph Laplacians},
year = {2005}
}
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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.
Keyphrases
graph laplacians combinatorial view graph partitioning reasonable consideration convergence property continuous manifold laplacian operator normalized laplacian different graph laplacian original graph different variant strong proof various method graph partitioning problem normalized laplacian encodes previous research graph laplacian unnormalized version semi-supervised learning spectral solution
