A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1200 |
| _version_ | 1797550061072154624 |
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| author | Ferdinando Di Martino Salvatore Sessa |
| author_facet | Ferdinando Di Martino Salvatore Sessa |
| author_sort | Ferdinando Di Martino |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:23:08Z |
| format | Article |
| id | doaj.art-df95042df60947f89c103231b2eefe7c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:23:08Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-df95042df60947f89c103231b2eefe7c2023-11-20T18:19:11ZengMDPI AGEntropy1099-43002020-10-012211120010.3390/e22111200A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering ProblemsFerdinando Di Martino0Salvatore Sessa1Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, ItalyDipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, ItalyTwo 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.https://www.mdpi.com/1099-4300/22/11/1200FCMvalidity indexfuzzy energyfuzzy entropy |
| spellingShingle | Ferdinando Di Martino Salvatore Sessa A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems Entropy FCM validity index fuzzy energy fuzzy entropy |
| title | A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems |
| title_full | A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems |
| title_fullStr | A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems |
| title_full_unstemmed | A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems |
| title_short | A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems |
| title_sort | new validity index based on fuzzy energy and fuzzy entropy measures in fuzzy clustering problems |
| topic | FCM validity index fuzzy energy fuzzy entropy |
| url | https://www.mdpi.com/1099-4300/22/11/1200 |
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