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Clustering With Pairwise Relationships: A Generative Approach

Yen-Yun Yu,S. Elhabian,R. Whitaker

Published 2018 in arXiv.org

ABSTRACT

Semi-supervised learning (SSL) has become important in current data analysis applications, where the amount of unlabeled data is growing exponentially and user input remains limited by logistics and expense. Constrained clustering, as a subclass of SSL, makes use of user input in the form of relationships between data points (e.g., pairs of data points belonging to the same class or different classes) and can remarkably improve the performance of unsupervised clustering in order to reflect user-defined knowledge of the relationships between particular data points. Existing algorithms incorporate such user input, heuristically, as either hard constraints or soft penalties, which are separate from any generative or statistical aspect of the clustering model; this results in formulations that are suboptimal and not sufficiently general. In this paper, we propose a principled, generative approach to probabilistically model, without ad hoc penalties, the joint distribution given by user-defined pairwise relations. The proposed model accounts for general underlying distributions without assuming a specific form and relies on expectation-maximization for model fitting. For distributions in a standard form, the proposed approach results in a closed-form solution for updated parameters.

PUBLICATION RECORD

  • Publication year

    2018

  • Venue

    arXiv.org

  • Publication date

    2018-05-06

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1805.02285
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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