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Flow-Based Dissimilarities: Shortest Path, Commute Time, Max-Flow and Free Energy

  • Guillaume Guex
  • François BavaudEmail author
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Random-walk based dissimilarities on weighted networks have demonstrated their efficiency in clustering algorithms. This contribution considers a few alternative network dissimilarities, among which a new max-flow dissimilarity, and more general flow-based dissimilarities, freely mixing shortest paths and random walks in function of a free parameter—the temperature. Their geometrical properties and in particular their squared Euclidean nature are investigated through their power indices and multidimensional scaling properties. In particular, formal and numerical studies demonstrate the existence of critical temperatures, where flow-based dissimilarities cease to be squared Euclidean. The clustering potential of medium range temperatures is emphasized.

Keywords

Short Path Random Walk Power Index Optimal Flow Commute Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of LausanneLausanneSwitzerland

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