Theories of Global Optimal and Minimal Solutions to K-means Cluster Analysis

摘要

K-means cluster analysis has been of fundamental importance in modern information processing, knowledge engineering, data mining, and data analysis. However the longstanding major problems with K-means clustering algorithms since the 1950s have been the local minima of clustering results. With larger data sets and more partitions, these non- or near -optimal solutions become worse, which seriously confines the K-means usabilities. As a milestone resolution to K-means issues, we announced our clustering methodology that is able to yield global optima or minima and now followed up with its underlying theories. They are conceptualized in a completely novel global partitioning model and circumvent all of the drawbacks associated with classical K-means. Based on this breakthrough in clustering theory, we introduced K-global optimum and minimum partitions (K-gomps) from the globality and integrity of data structure and object relationships. It was developed to a greater extent that makes the K-means clustering results really optimal. With our generation 3 of theories that is underpinning K-gomps, the goal to obtaining the clustering solution of highest quality has attained. The theories were validated by all implementations that successfully classifying any type/size of data sets as fast as possible into any number of disjoint clusters with a global minimum of total error sum of squares (TESS).