Transduction on Directed Graphs via Absorbing Random Walks

TL;DR

This paper introduces a novel random walk approach on directed graphs using absorbing Markov chains for transductive classification, effectively handling large-scale, sparse, and dynamic graphs while preserving directionality.

Contribution

It proposes a new method for directed graph transduction based on absorbing random walks, addressing limitations of undirected and symmetrized approaches.

Findings

Performs competitively against state-of-the-art methods

Handles large-scale and sparse directed graphs effectively

Maintains graph structure and weak signals in directed edges

Abstract

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs. In particular, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods.