How to Optimize Gower Distance Weights for the k-Medoids Clustering Algorithm to Obtain Mobility Profiles of the Swiss Population

This piece of research aims to obtain mobility profiles of the Swiss population. To that end, a survey of the Swiss Statistical Office (FSO) called Mobility and Transport Micro-census (MTMC) is utilized. Along with a qualitative method clustering, the respondents in the survey are clustered based on their mobility characteristics to obtain their profiles. The clustering, in particular acquiring medoids (centrotypes or exemplars), helps us then to generate a synthetic population of Switzerland. To gain medoids of each cluster, the k-Medoids clustering algorithm is utilized which partitions instances based on their positions in a latent space (symmetric distance matrix). Distances that shape this space can be generated by various metrics e.g. Euclidean, Gower, Manhattan. Since in this study features are mixed-type (e.g. numeric, categorical, etc.), the Gower distance metric is preferred. In this study, the default weights of the Gower distance are optimized to obtain a higher Average Silhouette Width (ASW) value of the clustering results. ASW can be used to measure the quality of clustering results in which high value leads to higher intra-cluster homogeneity and inter-cluster dissimilarity. So, maximizing the ASW value improves the quality of the clusters which is the goal of the optimization. At the end, this process helps us to obtain more accurate mobility profiles of the Swiss population.