Independence versus Indetermination: basis of two canonical clustering criteria

TL;DR

This paper compares two fundamental clustering criteria, based on optimal transport theory, highlighting their properties, differences, and implications for large network clustering.

Contribution

It introduces and analyzes two canonical couplings, 'statistical independence' and 'logical indetermination', providing a comparative framework for clustering methods.

Findings

The two couplings have similar results in network clustering.

Logical indetermination is less known but significant.

Estimated average difference explains their close clustering outcomes.

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.