Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure
The aim of this paper is to present a new approach to address the Fuzzy C Mean algorithm, which is considered one of the most important and famous algorithms that addressed the phenomenon of uncertainty in forming clusters according to the overlap ratios. One of the most important problems facing th...
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University of Baghdad, College of Science for Women
2024-09-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9516 |
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| author | Ahmed Husham Mohammed Marwan Abdul Hameed Ashour |
| author_facet | Ahmed Husham Mohammed Marwan Abdul Hameed Ashour |
| author_sort | Ahmed Husham Mohammed |
| collection | DOAJ |
| description | The aim of this paper is to present a new approach to address the Fuzzy C Mean algorithm, which is considered one of the most important and famous algorithms that addressed the phenomenon of uncertainty in forming clusters according to the overlap ratios. One of the most important problems facing this algorithm is its reliance primarily on the Euclidean distance measure, and by nature, the situation is that this measure makes the formed clusters take a spherical shape, which is unable to contain complex or overlapping cases. Therefore, this paper attempts to propose a new measure of distance, where we were able to derive a formula for the variance of the fuzzy cluster to be entered as a weight on the Euclidean Distance (WED) formula. Moreover, the calculation was processed partitions matrix through the use of the K-Means algorithm and creating a hybrid environment between the fuzzy algorithm and the sharp algorithm. To verify what was presented, experimental simulation was used and then applied to reality using environmental data for the physical and chemical examination of water testing stations in Basra Governorate. It was proven through the experimental results that the proposed distance measure Weighted Euclidean distance had the advantage over improving the work of the HFCM algorithm through the criterion (Obj_Fun, Iteration, Min_optimization, good fit clustering and overlap) when (c = 2,3) and according to the simulation results, c = 2 was chosen to form groups for the real data, which contributed to determine the best objective function (23.93, 22.44, 18.83) at degrees of fuzzing (1.2, 2, 2.8), while according to the degree of fuzzing (m = 3.6), the objective function for Euclidean Distance (ED) was the lowest, but the criteria were (Iter. = 2, Min_optimization = 0 and ) which confirms that (WED) is the best. |
| format | Article |
| id | doaj-art-67d8a62ff7014140a131fa56b19086bd |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-67d8a62ff7014140a131fa56b19086bd2025-08-20T03:56:19ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862024-09-0121910.21123/bsj.2024.9516Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure Ahmed Husham Mohammed0https://orcid.org/0000-0003-4384-6455Marwan Abdul Hameed Ashour 1https://orcid.org/0000-0001-8329-2894 Department of Statistics, College, College of Administration and Economics, University of Basrah, Basrah, Iraq. Department of Statistics, College, College of Administration and Economics, University of Baghdad, Baghdad, IraqThe aim of this paper is to present a new approach to address the Fuzzy C Mean algorithm, which is considered one of the most important and famous algorithms that addressed the phenomenon of uncertainty in forming clusters according to the overlap ratios. One of the most important problems facing this algorithm is its reliance primarily on the Euclidean distance measure, and by nature, the situation is that this measure makes the formed clusters take a spherical shape, which is unable to contain complex or overlapping cases. Therefore, this paper attempts to propose a new measure of distance, where we were able to derive a formula for the variance of the fuzzy cluster to be entered as a weight on the Euclidean Distance (WED) formula. Moreover, the calculation was processed partitions matrix through the use of the K-Means algorithm and creating a hybrid environment between the fuzzy algorithm and the sharp algorithm. To verify what was presented, experimental simulation was used and then applied to reality using environmental data for the physical and chemical examination of water testing stations in Basra Governorate. It was proven through the experimental results that the proposed distance measure Weighted Euclidean distance had the advantage over improving the work of the HFCM algorithm through the criterion (Obj_Fun, Iteration, Min_optimization, good fit clustering and overlap) when (c = 2,3) and according to the simulation results, c = 2 was chosen to form groups for the real data, which contributed to determine the best objective function (23.93, 22.44, 18.83) at degrees of fuzzing (1.2, 2, 2.8), while according to the degree of fuzzing (m = 3.6), the objective function for Euclidean Distance (ED) was the lowest, but the criteria were (Iter. = 2, Min_optimization = 0 and ) which confirms that (WED) is the best.https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9516Cluster, Distance measures, FCM, Fuzzy logic, Hybrid algorithm |
| spellingShingle | Ahmed Husham Mohammed Marwan Abdul Hameed Ashour Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure مجلة بغداد للعلوم Cluster, Distance measures, FCM, Fuzzy logic, Hybrid algorithm |
| title | Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure |
| title_full | Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure |
| title_fullStr | Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure |
| title_full_unstemmed | Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure |
| title_short | Enhancing Fuzzy C-Means Clustering with a Novel Standard Deviation Weighted Distance Measure |
| title_sort | enhancing fuzzy c means clustering with a novel standard deviation weighted distance measure |
| topic | Cluster, Distance measures, FCM, Fuzzy logic, Hybrid algorithm |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9516 |
| work_keys_str_mv | AT ahmedhushammohammed enhancingfuzzycmeansclusteringwithanovelstandarddeviationweighteddistancemeasure AT marwanabdulhameedashour enhancingfuzzycmeansclusteringwithanovelstandarddeviationweighteddistancemeasure |