A Weighted Quiver Kernel using Functor Homology

09/27/2020 ∙ by Manohar Kaul, et al. ∙ 2

In this paper, we propose a new homological method to study weighted directed networks. Our model of such networks is a directed graph Q equipped with a weight function w on the set Q_1 of arrows in Q. We require that the range W of our weight function is equipped with an addition or a multiplication, i.e., W is a monoid in the mathematical terminology. When W is equipped with a representation on a vector space M, the standard method of homological algebra allows us to define the homology groups H_*(Q,w;M). It is known that when Q has no oriented cycles, H_n(Q,w;M)=0 for n≥ 2 and H_1(Q,w;M) can be easily computed. This fact allows us to define a new graph kernel for weighted directed graphs. We made two sample computations with real data and found that our method is practically applicable.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 17

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.