Fractional Derivative to Symmetrically Extend the Memory of Fuzzy C-Means

被引:0
作者
Safouan, Safaa [1 ]
El Moutaouakil, Karim [1 ]
Patriciu, Alina-Mihaela [2 ]
机构
[1] Sidi Mohamed Ben Abdellah Univ, Multidisciplinary Fac Taza, Lab Engn Sci, Taza 35000, Morocco
[2] Dunarea De Jos Univ Galati, Fac Sci & Environm, Dept Math & Comp Sci, Galati 800201, Romania
来源
SYMMETRY-BASEL | 2024年 / 16卷 / 10期
关键词
fuzzy C-means; fractional derivative; genetic algorithm; GENETIC ALGORITHM; OPTIMIZATION; EQUATION; MODEL;
D O I
10.3390/sym16101353
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The fuzzy C-means (FCM) clustering algorithm is a widely used unsupervised learning method known for its ability to identify natural groupings within datasets. While effective in many cases, FCM faces challenges such as sensitivity to initial cluster assignments, slow convergence, and difficulty in handling non-linear and overlapping clusters. Aimed at these limitations, this paper introduces a novel fractional fuzzy C-means (Frac-FCM) algorithm, which incorporates fractional derivatives into the FCM framework. By capturing non-local dependencies and long memory effects, fractional derivatives offer a more flexible and precise representation of data relationships, making the method more suitable for complex datasets. Additionally, a genetic algorithm (GA) is employed to optimize a new least-squares objective function that emphasizes the geometric properties of clusters, particularly focusing on the Fukuyama-Sugeno and Xie-Beni indices, thereby enhancing the balance between cluster compactness and separation. Furthermore, the Frac-FCM algorithm is evaluated on several benchmark datasets, including Iris, Seed, and Statlog, and compared against traditional methods like K-means, SOM, GMM, and FCM. The results indicate that Frac-FCM consistently outperforms these methods in terms of the Silhouette and Dunn indices. For instance, Frac-FCM achieves higher Silhouette scores of most cases, indicating more distinct and well-separated clusters. Dunn's index further shows that Frac-FCM generates clusters that are better separated, surpassing the performance of traditional methods. These findings highlight the robustness and superior clustering performance of Frac-FCM. The Friedman test was employed to enhance and validate the effectiveness of Frac-FCM.
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页数:27
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