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NORMALIZED CUTS ARE APPROXIMATELY INVERSE EXIT TIMES.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2013, Vol. 34 Issue 2, p757-772. 16p. - Publication Year :
- 2013
-
Abstract
- Normalized cut is a widely used measure of separation between clusters in a graph. In this paper we provide a novel probabilistic perspective on this measure. We show that for a partition of a graph into two weakly connected sets, V = A ⊌ B, the multiway normalized cut is approximately MN cut ≈ 1/τA→B + 1/τB→A, where τA→B is the unidirectional characteristic exit time of a random walk from subset A to subset B. Using matrix perturbation theory, we show that this approximation is exact to first order in the connection strength between the two subsets A and B, and we derive an explicit bound for the approximation error. Our result implies that for a Markov chain composed of a reversible subset A that is weakly connected to an absorbing subset B, the easy-to-compute normalized cut measure is a reliable proxy for the chain's spectral gap. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 34
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 91878999
- Full Text :
- https://doi.org/10.1137/110826928