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A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems

1
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
2
Centro Interdipartimentale di Ricerca “Alberto Calza Bini”, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(11), 1200; https://doi.org/10.3390/e22111200
Received: 22 September 2020 / Revised: 13 October 2020 / Accepted: 21 October 2020 / Published: 23 October 2020
Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption. View Full-Text
Keywords: FCM; validity index; fuzzy energy; fuzzy entropy FCM; validity index; fuzzy energy; fuzzy entropy
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MDPI and ACS Style

Martino, F.D.; Sessa, S. A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems. Entropy 2020, 22, 1200. https://doi.org/10.3390/e22111200

AMA Style

Martino FD, Sessa S. A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems. Entropy. 2020; 22(11):1200. https://doi.org/10.3390/e22111200

Chicago/Turabian Style

Martino, Ferdinando D.; Sessa, Salvatore. 2020. "A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems" Entropy 22, no. 11: 1200. https://doi.org/10.3390/e22111200

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