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Clustering Analysis of a Dissimilarity: a Review of Algebraic and Geometric Representation

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  • D. Fortin

    (Inria)

Abstract

It is customary to split clustering analysis into an optimization level, then a (preferably) graphical representation level to take benefit of human vision for an effective understanding of (big) data structure. This article aspires to clarify relationships between clustering, both its process and its representation, and the underlying structural graph properties, both algebraic and geometric, starting from the mere knowledge of a dissimilarity matrix among items, possibly with missing entries. It is inspired by an analogous work on seriation problem, relating Robinson property in a dissimilarity with missing entries, with interval graph recognition using a sequence of 4 lexicographic breadth first searches.

Suggested Citation

  • D. Fortin, 2020. "Clustering Analysis of a Dissimilarity: a Review of Algebraic and Geometric Representation," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 180-202, April.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:1:d:10.1007_s00357-019-09315-7
    DOI: 10.1007/s00357-019-09315-7
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    References listed on IDEAS

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    1. D. Fortin, 2017. "Robinsonian Matrices: Recognition Challenges," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 191-222, July.
    2. Libor Buš & Pavel Tvrdík, 2009. "Towards auction algorithms for large dense assignment problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 411-436, July.
    Full references (including those not matched with items on IDEAS)

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