Independence versus Indetermination: basis of two canonical clustering criteria

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 Monges 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.