An Investigation into Distance Measures in Cluster Analysis

Abstract: This report provides an exploration of different distance measures that can be used with the $K$-means algorithm for cluster analysis. Specifically, we investigate the Mahalanobis distance, and critically assess any benefits it may have over the more traditional measures of the Euclidean, Manhattan and Maximum distances. We perform this by first defining the metrics, before considering their advantages and drawbacks as discussed in literature regarding this area. We apply these distances, first to some simulated data and then to subsets of the Dry Bean dataset [1], to explore if there is a better quality detectable for one metric over the others in these cases. One of the sections is devoted to analysing the information obtained from ChatGPT in response to prompts relating to this topic.