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Independence versus indetermination: basis of two canonical clustering criteria

Author

Listed:
  • Pierre Bertrand

    (Sorbonne Université)

  • Michel Broniatowski

    (Sorbonne Université)

  • Jean-François Marcotorchino

    (Sorbonne Université)

Abstract

This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use “optimal transport theory” as a starting point, and a way as well, to derive two canonical couplings: “statistical independence” and “logical indetermination”. A symmetric list of properties is provided and notably the so called “Monge’s properties”, applied to contingency matrices, and justifying the $$\otimes $$ ⊗ versus $$\oplus $$ ⊕ notation. A study is proposed, highlighting “logical indetermination”, because it is, by far, lesser known. Eventually we estimate the average difference between both couplings as the key explanation of their usually close results in network clustering.

Suggested Citation

  • Pierre Bertrand & Michel Broniatowski & Jean-François Marcotorchino, 2022. "Independence versus indetermination: basis of two canonical clustering criteria," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 1069-1093, December.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:4:d:10.1007_s11634-021-00484-1
    DOI: 10.1007/s11634-021-00484-1
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    References listed on IDEAS

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