Low-distortion inference of latent similarities from a multiplex social network

Ittai Abraham*, Shiri Chechik, David Kempe, Aleksandrs Slivkins

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

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 a near-linear time algorithm which reconstructs each metric with provably low distortion.

Original languageEnglish
Title of host publicationProceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
PublisherAssociation for Computing Machinery
Pages1853-1872
Number of pages20
ISBN (Print)9781611972511
DOIs
StatePublished - 2013
Externally publishedYes
Event24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 - New Orleans, LA, United States
Duration: 6 Jan 20138 Jan 2013

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
Country/TerritoryUnited States
CityNew Orleans, LA
Period6/01/138/01/13

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