Multi-way dual Cheeger constants and spectral bounds of graphs |
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Authors: | Shiping Liu |
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Institution: | Department of Mathematical Sciences, Durham University, DH1 3LE Durham, United Kingdom |
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Abstract: | We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum. |
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Keywords: | Cheeger constants Higher-order dual Cheeger inequalities Spectral clustering Markov operators Essential spectrum |
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