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.
Campagner, A., Ciucci, D. (2020). A Formal Learning Theory for Three-Way Clustering. In Scalable Uncertainty Management 14th International Conference, SUM 2020, Bozen-Bolzano, Italy, September 23–25, 2020, Proceedings (pp.128-140). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-58449-8_9].
A Formal Learning Theory for Three-Way Clustering
Campagner, Andrea
;Ciucci, Davide
2020
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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