A Necessary Condition about the Optimum Partition on a Finite Set of Samples and Its Application to Clustering Analysis

This paper presents another necessary condition about the optimum parti-tion on a finite set of samples. From this condition, a corresponding generalized sequential hao f k-means (GSHKM) clustering algorithm is built and many well-known clustering algorithms are found to be included in it. Under some assumptions the well-known MacQueen's SHKM (Sequential Hard K-Means)algorithm, FSCL (Frequency Sensitive Competitive Learning) algorithm and RPCL (Rival Penalized Competitive Learning) algorithm are derived. It…