A Multi-objective Approach for Inter-cluster and Intra-cluster Distance Analysis for Numeric Data

Abstract

AbstractA measure of how closely a set of data items are connected is determined based on the similarity or dissimilarity between the data items. Inter-cluster and intra-cluster distances are two metrics that exhibit how the data items can group accordingly to form clusters. Usually, the data items with high similarities are in the same cluster, and the distance between them is significantly less. A good clustering algorithm always maintains high similarity within the cluster, thereby maximizing the distance between the data items having higher dissimilarities in distinct clusters. These measures play a crucial role in identifying the patterns among the data objects. Euclidean distance acts as a distance measure for determining these two metrics. This paper proposes a multi-objective approach for clustering to establish the relationship between inter-cluster and intra-cluster distances. It aims to perform a comparative analysis of the sum of inter-cluster and intra-cluster distances. It reveals that when the sum of intra-cluster distance is minimizing, then the sum of inter-cluster distance is maximizing for a given dataset.KeywordsClusteringK-meansIntra-cluster and inter-cluster distanceMulti-objective