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A Formal Learning Theory for Three-Way Clustering

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Scalable Uncertainty Management (SUM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12322))

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Abstract

In this work, we study the theoretical properties, from the perspective of learning theory, of three-way clustering and related formalisms, such as rough clustering or interval-valued clustering. In particular, we generalize to this setting recent axiomatic characterization results that have been discussed for classical hard clustering. After proposing an axiom system for three-way clustering, which we argue is a compatible weakening of the traditional hard clustering one, we provide a constructive proof of an existence theorem, that is, we show an algorithm which satisfies the proposed axioms. We also propose an axiomatic characterization of the three-way k-means algorithm family and draw comparisons between the two approaches.

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Authors and Affiliations

  1. Università degli Studi di Milano-Bicocca, Milan, Italy

    Andrea Campagner & Davide Ciucci

Authors
  1. Andrea Campagner
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  2. Davide Ciucci
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Corresponding author

Correspondence to Andrea Campagner .

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Editors and Affiliations

  1. KU Leuven, Heverlee, Belgium

    Jesse Davis

  2. Artois University, Lens, France

    Karim Tabia

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Campagner, A., Ciucci, D. (2020). A Formal Learning Theory for Three-Way Clustering. In: Davis, J., Tabia, K. (eds) Scalable Uncertainty Management. SUM 2020. Lecture Notes in Computer Science(), vol 12322. Springer, Cham. https://doi.org/10.1007/978-3-030-58449-8_9

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  • DOI: https://doi.org/10.1007/978-3-030-58449-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58448-1

  • Online ISBN: 978-3-030-58449-8

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