Correlation clustering

N. Bansal, A. Blum, S. Chawla

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

    158 Citations (Scopus)

    Abstract

    We consider the following clustering problem: we have a complete graph on n vertices (items), where each edge (u; v) is labeled either + or - depending on whether u and v have been deemed to be similar or different. The goal is to produce a partition of the vertices (a clustering) that agrees as much as possible with the edge labels. That is, we want a clustering that maximizes the number of + edges within clusters, plus the number of - edges between clusters (equivalently, minimizes the number of disagreements: the number of - edges inside clusters plus the number of + edges between clusters). This formulation is motivated from a document clustering problem in which one has a pairwise similarity function f learned from past data, and the goal is to partition the current set of documents in a way that correlates with f as much as possible; it can also be viewed as a kind of "agnostic learning" problem. An interesting feature of this clustering formulation is that one does not need to specify the number of clusters k as a separate parameter, as in measures such as k-median or min-sum or min-max clustering. Instead, in our formulation, the optimal number of clusters could be any value between 1 and n, depending on the edge labels. We look at approximation algorithms for both minimizing disagreements and for maximizing agreements. For minimizing disagreements, we give a constant factor approximation. For maximizing agreements we give a PTAS. We also show how to extend some of these results to graphs with edge labels in [-1, +1] and give some results for the case of random noise.
    Original languageEnglish
    Title of host publicationProceedings of the 43rd Annual IEEE Sympiosium on Foundations of Computer Science (FOCS'02, Vancouver BC, Canada, November 16-19, 2002)
    PublisherInstitute of Electrical and Electronics Engineers
    Pages238-250
    ISBN (Print)0-7695-1822-2
    Publication statusPublished - 2002

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