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Entropy 2019, 21(2), 196; https://doi.org/10.3390/e21020196

Centroid-Based Clustering with αβ-Divergences

Departamento de Teoría de la Señal y Comunicaciones, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los descubrimientos, S/N, 41092 Sevilla, Spain
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Received: 18 January 2019 / Revised: 6 February 2019 / Accepted: 14 February 2019 / Published: 19 February 2019
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Abstract

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 α β -divergences, which is governed by two parameters, α and β . We propose a new iterative algorithm, α β -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 ( α , β ). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ( α , β ) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications. View Full-Text
Keywords: αβ-divergence; k-means algorithm; centroid-based clustering; musical genre clustering; unsupervised classification αβ-divergence; k-means algorithm; centroid-based clustering; musical genre clustering; unsupervised classification
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Sarmiento, A.; Fondón, I.; Durán-Díaz, I.; Cruces, S. Centroid-Based Clustering with αβ-Divergences. Entropy 2019, 21, 196.

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