Independence versus indetermination: basis of two canonical clustering criteria

Pierre Bertrand (), Michel Broniatowski () and Jean-François Marcotorchino
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Pierre Bertrand: Sorbonne Université
Michel Broniatowski: Sorbonne Université
Jean-François Marcotorchino: Sorbonne Université

Advances in Data Analysis and Classification, 2022, vol. 16, issue 4, No 10, 1069-1093

Abstract: 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.

Keywords: Correlation clustering; Mathematical relational analysis; Logical indetermination; Coupling functions; Optimal transport; Graph theoretical approaches; 97N70; 91C20; 97K50; 97K80 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11634-021-00484-1

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