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Centroid-Based Clustering with αβ-Divergences

Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures...

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Autores principales: Sarmiento, Auxiliadora, Fondón, Irene, Durán-Díaz, Iván, Cruces, Sergio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514678/
https://www.ncbi.nlm.nih.gov/pubmed/33266911
http://dx.doi.org/10.3390/e21020196
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author Sarmiento, Auxiliadora
Fondón, Irene
Durán-Díaz, Iván
Cruces, Sergio
author_facet Sarmiento, Auxiliadora
Fondón, Irene
Durán-Díaz, Iván
Cruces, Sergio
author_sort Sarmiento, Auxiliadora
collection PubMed
description Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of [Formula: see text]-divergences, which is governed by two parameters, [Formula: see text] and [Formula: see text]. We propose a new iterative algorithm, [Formula: see text]-k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair ([Formula: see text]). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ([Formula: see text]) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.
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spelling pubmed-75146782020-11-09 Centroid-Based Clustering with αβ-Divergences Sarmiento, Auxiliadora Fondón, Irene Durán-Díaz, Iván Cruces, Sergio Entropy (Basel) Article Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of [Formula: see text]-divergences, which is governed by two parameters, [Formula: see text] and [Formula: see text]. We propose a new iterative algorithm, [Formula: see text]-k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair ([Formula: see text]). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ([Formula: see text]) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications. MDPI 2019-02-19 /pmc/articles/PMC7514678/ /pubmed/33266911 http://dx.doi.org/10.3390/e21020196 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Sarmiento, Auxiliadora
Fondón, Irene
Durán-Díaz, Iván
Cruces, Sergio
Centroid-Based Clustering with αβ-Divergences
title Centroid-Based Clustering with αβ-Divergences
title_full Centroid-Based Clustering with αβ-Divergences
title_fullStr Centroid-Based Clustering with αβ-Divergences
title_full_unstemmed Centroid-Based Clustering with αβ-Divergences
title_short Centroid-Based Clustering with αβ-Divergences
title_sort centroid-based clustering with αβ-divergences
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514678/
https://www.ncbi.nlm.nih.gov/pubmed/33266911
http://dx.doi.org/10.3390/e21020196
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