A Combinatorial View of Graph Laplacians
نویسنده
چکیده
Discussions about different graph Laplacians—mainly the normalized and unnormalized versions of graph Laplacian—have been ardent with respect to various methods of clustering and graph based semi-supervised learning. Previous research in the graph Laplacians, from a continuous perspective, investigated the convergence properties of the Laplacian operators on Riemannian Manifolds. In this paper, we analyze different variants of graph Laplacians directly by solving the original NP hard graph partitioning problems that provides a combinatorial point of view of graph Laplacians. The spectral solutions provide evidence that the normalized Laplacian encodes more reasonable considerations for graph partitioning. We also explain the direct relationship between spectral clustering and graph-based semi-supervised learning. We provide experiments comparing the results of using different graph Laplacians.
منابع مشابه
A Combinatorial View of the Graph Laplacians
Discussions about different graph Laplacians, mainly normalized and unnormalized versions of the graph Laplacians, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on the graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence...
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