Next Article in Journal
Magnetotelluric Signal-Noise Identification and Separation Based on ApEn-MSE and StOMP
Next Article in Special Issue
Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment
Previous Article in Journal
Spatial Organization of the Gene Regulatory Program: An Information Theoretical Approach to Breast Cancer Transcriptomics
Previous Article in Special Issue
New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessFeature PaperArticle
Entropy 2019, 21(2), 196;

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
Authors to whom correspondence should be addressed.
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)
Full-Text   |   PDF [956 KB, uploaded 19 February 2019]   |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Sarmiento, A.; Fondón, I.; Durán-Díaz, I.; Cruces, S. Centroid-Based Clustering with αβ-Divergences. Entropy 2019, 21, 196.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top