A Deterministic Hitting-Time Moment Approach to Seed-set Expansion over a Graph

TL;DR

HITMIX is a scalable, deterministic method that uses hitting-time moments to statistically identify vertices related to a seed set in large graphs, outperforming local methods in solution quality.

Contribution

The paper introduces HITMIX, the first full statistical model for seed-set expansion that provides vertex-level membership probabilities using hitting-time moments.

Findings

HITMIX effectively identifies related vertices in large graphs.

It outperforms existing local methods in solution quality.

The method is scalable and suitable for large, in-memory graphs.

Abstract

We introduce HITMIX, a new technique for network seed-set expansion, i.e., the problem of identifying a set of graph vertices related to a given seed-set of vertices. We use the moments of the graph's hitting-time distribution to quantify the relationship of each non-seed vertex to the seed-set. This involves a deterministic calculation for the hitting-time moments that is scalable in the number of graph edges and so avoids directly sampling a Markov chain over the graph. The moments are used to fit a mixture model to estimate the probability that each non-seed vertex should be grouped with the seed set. This membership probability enables us to sort the non-seeds and threshold in a statistically-justified way. To the best of our knowledge, HITMIX is the first full statistical model for seed-set expansion that can give vertex-level membership probabilities. While HITMIX is a global method, its linear computation complexity in practice enables computations on large graphs. We have a high-performance implementation, and we present computational results on stochastic blockmodels and a small-world network from the SNAP repository. The state of the art in this problem is a collection of recently developed local methods, and we show that distinct advantages in solution quality are available if our global method can be used. In practice, we expect to be able to run HITMIX if the graph can be stored in memory.