Representation of functions on big data associated with directed graphs

TL;DR

This paper extends function representation methods from undirected to directed graphs, introducing new mathematical tools and algorithms, with experimental validation on datasets like CORA, Proposition, and Wiki-votes.

Contribution

It develops theoretical and algorithmic frameworks for representing functions on directed graphs, expanding previous work from numeric to non-numeric data.

Findings

Effective data-dependent orthogonal systems for digraphs

Successful application to real-world datasets

Enhanced theoretical understanding of function analysis on digraphs

Abstract

This paper is an extension of the previous work of Chui, Filbir, and Mhaskar (Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called digraphs, for simplicity). Besides theoretical development, this paper introduces effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs. In addition, this paper also includes algorithmic development and discussion of various experimental results on such data-sets as CORA, Proposition, and Wiki-votes.