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Cluster Analysis by Restricted Random Walks

  • Joachim Schöll
  • Elisabeth Paschinger
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A new graph theoretical method is introduced to analyze a data set of objects described by a dissimilarity matrix d ij . This method is based on the generation of a series of random walks in the data set. We define a random walk in a data set by moving in each time step from one object to another one at random. In order that the random walk depends on the pattern of the data, a restriction depending on the previous moves is imposed during its generation, so that the random walk is attracted by clusters formed of similar objects. We define a hierarchical set of graphs consisting of all connections of a series of random walks at a certain time step to detect the structure of the data and to derive an similarity measure between the objects. In an example an application of the method is shown.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joachim Schöll
    • 1
  • Elisabeth Paschinger
    • 2
  1. 1.Institut für Statistik und WahrscheinlichkeitstheorieTU WienWienÖsterreich
  2. 2.Institut für Theoretische PhysikTU WienWienÖsterreich

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