An analysis of the Used Lead Acid Battery (ULAB) collection network in Mauritius, using the ESMvere- R-hamming-k-median clustering method

This research examines the challenge of hazardous waste management from Used Lead Acid Batteries (ULABs) in Mauritius, a pressing public health and environmental concern due to the risks of lead exposure. To the best of our knowledge for two decades now, there has not been any research about the level of lead poisoning contamination from the ULABs in the Mauritian environment. Thus, research or efforts to cautiously eliminate ULABs, which are one of the main causes of lead poisoning, are missing in the literature. This paper focuses on the analysis of a survey on the ULAB disposal system and probes the need to establish a new ULAB collection system. The research describes the analysis of a questionnaire dataset and contributes a novel clustering method to identify and interpret the clusters of respondents. The new method ascribes a numerical value to the best choice of the number of clusters k, when using the k-median hamming distance metric. To the best of our knowledge this is usually the most complex decision when clustering data using either the k-means or its variant the k-median. There is a need to be sure of the optimum number of clusters that give the best value of the k. The novel method uses the k-median clustering method, which is a popular choice because of its robustness and resistance to outliers. The best choice of the number of clusters is explored through an iteration of different values of k, obtaining a numerical value in each iteration thus enabling a comparison among the iterations. This value determines the measure of the best clustering performance. The data in each iteration is visualized using silhouette plots. The new method uses the Average silhouette width numerical value to simplify the choice of the best number of clusters k. The R Language was used to develop the new method. The results showed that 55% of the respondents strongly agreed that there is a need to develop a new collection system.