I apologize for this quite abstract question, I am asking it because I am getting nowhere in my research of the topic (but I can’t imagine I’m the first one to consider this). I hope the below makes sense:

I am searching for a formalism in which to describe interactions consisting of N elements, N > 2. In my work, I have repeatedly been considering nonlinear functions defined on S^M, S some set of elements. Until now I have been trying to use network models, with each node representing an element in S. However, this seems to be primarily suited for M=2, at least it seems I have to make a great deal of extra assumptions to properly study M-groups on a network.

A concrete example that I was considering today is feature selection from a large number of possible features, in relation to machine learning. This is an example of a non-linear knapsack problem, and some heuristic is needed to search for the optimal set of features. An interesting take could be to move around in S^M, but that requires some sort of metric to determine which sets of features are close (simply moving around {0,1}^(#elements in S) would amount to brute-forcing the problem).

In short, it seems there are various problems that I tend to think of as being structured around groups larger than 2, and where a good way to describe them could be useful. I am not looking for a solution to my above problem, but it would be nice to have some better keywords to google for inspiration, or at least some terminology for describing the situation.

TLDR.:

Imagine a network where edges connect M nodes instead of two. What do we call that?

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a good example of how much at a loss I am is that I don’t even know what tags to put on this 😉

– Kaare

2 days ago

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1 Answer

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The sructure you are describing is called a hypergraph, they do not have a whole lot of structure so not a lot of things can be said about them generally. You may also be interested in combinatorial designs, matroids or Simplicial Complices.