Some Advances in Role Discovery in Graphs

TL;DR

This paper introduces a supervised, flexible framework for role discovery in graphs, extending to multi-relational graphs using tensor decompositions, overcoming limitations of previous unsupervised, single-relational methods.

Contribution

It proposes an alternating least squares framework with convex constraints for supervised role discovery and extends it to multi-relational graphs via Tucker tensor decomposition.

Findings

Framework allows supervision through sparsity, diversity, and alternativeness constraints.

New tensor decomposition algorithm tailored for multi-relational role discovery.

Demonstrates practical usefulness of the proposed methods.

Abstract

Role discovery in graphs is an emerging area that allows analysis of complex graphs in an intuitive way. In contrast to other graph prob- lems such as community discovery, which finds groups of highly connected nodes, the role discovery problem finds groups of nodes that share similar graph topological structure. However, existing work so far has two severe limitations that prevent its use in some domains. Firstly, it is completely unsupervised which is undesirable for a number of reasons. Secondly, most work is limited to a single relational graph. We address both these lim- itations in an intuitive and easy to implement alternating least squares framework. Our framework allows convex constraints to be placed on the role discovery problem which can provide useful supervision. In par- ticular we explore supervision to enforce i) sparsity, ii) diversity and iii) alternativeness. We then show how to lift this work for multi-relational graphs. A natural representation of a multi-relational graph is an order 3 tensor (rather than a matrix) and that a Tucker decomposition allows us to find complex interactions between collections of entities (E-groups) and the roles they play for a combination of relations (R-groups). Existing Tucker decomposition methods in tensor toolboxes are not suited for our purpose, so we create our own algorithm that we demonstrate is pragmatically useful.