Distributed Clustering in Wireless Sensor Network with Kernel Based Weighted Fuzzy C-Means Algorithm

The main limitation of the Fuzzy C-Means technique is its sensitivity to noise and outliers, which limits its use in adverse clustering scenarios. The new framework reported in this manuscript is based on kernel-induced distance matric using the Gaussian Radial Basis Function (GRBF), and the proposed algorithm is named as Distributed Kernel-based Weighted Fuzzy C-Means (DKWFCM) algorithm. In wireless sensor networks (WSN), Distributed approaches perform the clustering task across network nodes, mitigating privacy risks, reducing communication overhead, and adapting to network dynamics. Feature-weight and cluster-weight learning are incorporated for more effective cluster analysis in distributed environments. Additionally, DKWFCM leverages diffusion-based learning to enable information processing across multiple wireless sensor nodes. The proposed algorithm DKWFCM performance is evaluated on synthetic and real-world datasets distributed over six wireless sensor nodes. Five datasets for validation which consists of two Synthetic datasets (Circle_3_2, Mixed_3_2) and three real-world datasets (the Cook Agricultural land dataset, Thames River water quality dataset, and Canada Weather station dataset). Performance is assessed using the Silhouette Index (SI) and Dunn Index (DI) as a validation measures. Simulation results demonstrated the superior performance of DKWFCM over traditional FCM algorithms such as Distributed FCM (DFCM) algorithm and Distributed Weighted FCM (DWFCM). The superiority is evident in various aspects, such as visual clusters obtained at each node, SI value, DI value plots at the sensor nodes, and average convergence plots. The minimum value of average Euclidean deviation of proposed DKWFCM optimization algorithm is reduced by 27.73%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 31.86%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} and 10.11%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 19.40%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} compared to DFCM and DWFCM respectively for both synthetic datasets. Similarly, it is reduced by 99.12%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 97.13%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 54.29%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} and 5.69%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 91.67%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}; 30.41%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} respectively for the three real-world datasets. These findings suggest that the proposed algorithm DKWFCM improves cluster analysis in distributed processing environments of WSNs.