A polynomial algorithm for balanced clustering via graph partitioning

Abstract The objective of clustering is to discover natural groups in datasets and identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics data. problem can be seen as detecting inherent separations between a given point set metric space governed by similarity function. pairwise similarities all data objects form weighted graph whose adjacency matrix contains necessary information for process. Consequently, task formulated partitioning problem. In this context, we propose new cluster quality measure uses ratio intra- inter-cluster variance allows us compute optimal under min-max principle polynomial time. Our algorithm applied both partitional hierarchical clustering.