2020/09/27 by Manohar Kaul, Kaul, Manohar, Dai Tamaki +1
Computer Science · Mathematics · #Advanced Graph Neural Networks #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Tensor decomposition and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2009.12928
openalex publication_date 2020/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Q1 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, Hn(Q,w;M)=0 for n≥ 2 and H1(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.