k-Medoids Substitution Clustering Method and a New Clustering Validity Index Method

It introduces a k-medoids substitution clustering method based on the idea of simplex method after discussing k-means and k-medoids. This algorithm is more effective and less sensitive to initial medoids sets than k-means or k-medoids based on analysis of the discrepancy of searching policy and simulation experiment results, when clustering those data-point sets with some similar-sized clusters. The experimental figures, which illustrates the relationship between the final average value of the clustering objective function and the number of the clusters, shows as an experimental rule that the optimal number of clusters often locates at a corner position where the quickly degressive segment of the final average value of the clustering objective function turns to the slowly degressive segment with the step-by-step increasing of the number of the clusters. Obviously, this experimental rule is more encouraging and intuitive to understand