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 networksdecomposition, 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 .
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 .
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very large graphs. Although the scientific literature is not sparing with clustering criteria dedicated to graphs and networksdecomposition, 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
and clustering very large networks. We
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then we will derive two main families of criteria: those based upon
and a way as well, to derive two canonical couplings:
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versus those based upon
and
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indetermina-tion
indetermination
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Among others, we will use
A symmetric list of properties is provided and notably
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context, as specific tricks for putting forward some key features about those criteria. A further and deeper
, and justifying the \otimes versus \oplus notation. A
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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
Eventually we estimate the average difference between both couplings as the key explanation of their usually close results in network clustering