How Good is the Euclidean Distance Metric for the Clustering Problem

Data Mining is concerned with the discovery of interesting patterns and knowledge in data repositories. Cluster Analysis which belongs to the core methods of data mining is the process of discovering homogeneous groups called clusters. Given a data-set and some measure of similarity between data objects, the goal in most clustering algorithms is maximizing both the homogeneity within each cluster and the heterogeneity between different clusters. In this work, test cases are used to demonstrate that the Euclidean Distance widely in literature is not a suitable metric for capturing the quality of the clustering.