Low-distortion Inference of Latent Similarities from a Multiplex Social Network

TL;DR

This paper introduces an algorithm to accurately reconstruct latent similarity metrics from multiplex social networks, which are unions of multiple underlying categories, with provably low distortion.

Contribution

It formalizes the problem of inferring latent social space metrics from multiplex networks and provides a novel algorithm with theoretical guarantees for low-distortion reconstruction.

Findings

Algorithm achieves low distortion in reconstructing latent metrics.

Applicable to Kleinberg's small world model and variations.

Provides theoretical bounds on reconstruction accuracy.

Abstract

Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the latent underlying "social space:" the way in which individuals are similar or dissimilar. Many research questions frequently addressed via social network analysis are in reality questions about this social space, raising the question of inverting the process: Given a social network, how accurately can we reconstruct the social structure of similarities and dissimilarities? We begin to address this problem formally. Observed social networks are usually multiplex, in the sense that they reflect (dis)similarities in several different "categories," such as geographical proximity, kinship, or similarity of professions/hobbies. We assume that each such category is characterized by a latent metric capturing (dis)similarities in this category. Each category gives rise to a separate social network: a random graph parameterized by this metric. For a concrete model, we consider Kleinberg's small world model and some variations thereof. The observed social network is the unlabeled union of these graphs, i.e., the presence or absence of edges can be observed, but not their origins. Our main result is an algorithm which reconstructs each metric with provably low distortion.