Learning Mixed Membership from Adjacency Graph Via Systematic Edge Query: Identifiability and Algorithm

Abstract

Graph clustering is a core technique for network analysis problems, e.g., community detection. This work puts forth a node clustering approach for largely incomplete adjacency graphs. Under the considered scenario, instead of having access to the complete graph, only a small amount of queries about the graph edges can be made for node clustering. This task is well-motivated in many large-scale network analysis problems, where complete graph acquisition is prohibitively costly. Prior work tackles this problem under the setting that the nodes only admit single membership and the clusters are disjoint, yet multiple membership nodes and overlapping clusters often arise in practice. Existing approaches also rely on random edge query patterns and convex optimization-based formulations, which give rise to a number of implementation and scalability challenges. This work offers a framework that provably learns the mixed membership of nodes from overlapping clusters using limited edge information. Our method is equipped with a systematic edge query pattern, which is arguably easier to implement relative to the random counterparts in certain applications, e.g., field survey based graph analysis. A lightweight scalable algorithm is proposed, and its performance characterizations are presented. Numerical experiments are used to showcase the effectiveness of our method.

Learning From Crowds With Contrastive Representation

“…Our framework is inclusive of existing crowdsourcing approaches. The loss here can be replaced by other existing work, such as TraceReg [36] and GeoCrowdNet [18].…”

“…The end-to-end approach has attracted more attention due to its simple structure and decent performance in practice. Although massive efforts have been made to consummate the basic end-to-end model, such as adopting a more effective annotator layer [18] and modeling the interactions between annotators and instances [19], how to learn better instance representation from crowd-labeled data has been neglected for a long time.…”

Mixed Membership Graph Clustering via Systematic Edge Query

“…An initial and limited version of this work was submitted to IEEE ICASSP 2021 [21]. In this journal version, we additionally include (1) detailed identifiability analysis of the proposed algorithm (Theorem 1 and its proof); (2) the integrated performance characterization of the SVD and SSMF stages (Theorem 2 and its proof); (3) a new application, namely, crowdclustering; (4) a series of new real-data experiments; (5) and a newly acquired dataset for crowdclustering that is made publicly available.…”

“…To make the above derivation legitimate, we need the assumptions in Lemma 1-6 hold true. The assumptions on C r in Lemma 1 given by the equalities in (21)…”