"Statistical Independence" versus "Logical Indetermination", two ways of generating clustering criteria through couplings : Application to graphs modularization
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This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing very large graphs. Although the scientific literature is not sparing with clustering criteria dedicated to graphs and networks decomposition, we shall nevertheless rework this subject, in this paper, by proposing a new symmetric and dual approach based on coupling functions, allowing to compare and calibrate them. To elaborate those coupling maps, we will briefly use "optimal transport theory" as a starting point, then we will derive two main families of criteria: those based upon "statistical independence" versus those based upon "logical indetermina-tion". Among others, we will use the so called "Monge's properties", applied to contingency matrices context, as specific tricks for putting forward some key features about those criteria. A further and deeper study is proposed, highlighting "logical indetermination", because it is, by far, lesser known. Those dual and parallel criteria are perfectly suited for graphs clustering, this will be illustrated and shown on various types of graphs within this paper.
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