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Efficiency of Transformations of Proximity Measures for Graph Clustering

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Algorithms and Models for the Web Graph (WAW 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11631))

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Abstract

Choice of proximity measure for the nodes greatly affects the results of graph clustering. In this paper, we consider several proximity measures transformed with a number of functions including the logarithmic function, the power function, and a family of activation functions. Transformations are tested in experiments in which several classical datasets are clustered using the k-Means, Ward, and the spectral method. The analysis of experimental results with statistical methods shows that a number of transformed proximity measures outperform their non-transformed versions. The top-performing transformed measures are the Heat measure transformed with the power function, the Forest measure transformed with the power function, and the Forest measure transformed with the logarithmic function.

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Notes

  1. 1.

    Hereinafter, a clustering algorithm is denoted by such a triplet. The first element in a triplet is a clustering method, the second is a proximity measure, and the third is a transformation.

  2. 2.

    Recall that an algorithm here refers to a triplet: a clustering method, a proximity measure, and a transformation.

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Author information

Authors and Affiliations

  1. Kotel’nikov Institute of Radio-engineering and Electronics (IRE) of Russian Academy of Sciences, Mokhovaya 11-7, Moscow, 125009, Russia

    Rinat Aynulin

  2. Moscow Institute of Physics and Technology, 9 Inststitutskii per., Dolgoprudny, Moscow Region, 141700, Russia

    Rinat Aynulin

Authors
  1. Rinat Aynulin
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Corresponding author

Correspondence to Rinat Aynulin .

Editor information

Editors and Affiliations

  1. Inria, Sophia Antipolis, France

    Konstantin Avrachenkov

  2. Ryerson University, Toronto, ON, Canada

    Paweł Prałat

  3. The University of Queensland, Brisbane, QLD, Australia

    Nan Ye

Appendices

Appendix A

CD-diagrams

Fig. 5.
figure 5

The CD-diagrams for the algorithms based on the k-Means method

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Fig. 6.
figure 6

The CD-diagrams for the algorithms based on the spectral method

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Aynulin, R. (2019). Efficiency of Transformations of Proximity Measures for Graph Clustering. In: Avrachenkov, K., Prałat, P., Ye, N. (eds) Algorithms and Models for the Web Graph. WAW 2019. Lecture Notes in Computer Science(), vol 11631. Springer, Cham. https://doi.org/10.1007/978-3-030-25070-6_2

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  • DOI: https://doi.org/10.1007/978-3-030-25070-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25069-0

  • Online ISBN: 978-3-030-25070-6

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