Fuzzy C-Means Algorithm Modification Based on Distance Measurement for River Water Quality

Abstract

River water quality could be determined by understanding the capacity of pollutants in a water body. Fuzzy C-Means (FCM) is one of the fuzzy clustering methods for determining river water quality by measuring water quality parameters, that is, dissolved oxygen (DO) and total dissolved solids (TDS). The FCM algorithm is an effective fuzzy clustering algorithm for grouping data but often produces local and inconsistent optimal solutions due to the partition matrix's random initialisation process. Therefore, this study proposes to modify the FCM algorithm to be precise in the partition matrix initialisation process using several distance concepts. The purpose of the proposed algorithm modification is to get more consistent FCM clustering results and minimise stop iterations. The validation process for the clustering results uses the FCM algorithm, and the FCM modification algorithm uses three parameters, namely the Partition Coefficient Index (PCI), Partition Entropy Index (PEI) and Silhouette Score (SS). The experiments were conducted with three replications and using various distance concepts. The results showed that the number of iterations stopped in the FCM algorithm has different values for PCI, PEI, SS, and stop iterations and objective functions in each trial. On the contrary, the FCM modification algorithm has consistent PCI, PEI, and SS values, and the number of iterations stops with fewer iterations. Therefore, the modified algorithm for initialising the partition matrix can be used in the fuzzy C-means clustering algorithm.