AN OPTIMAL SOLUTION APPROACH FOR THE K-MEDOIDS CLUSTERING BASED ON MATHMATICAL PROGRAMMING

All k-medoids clustering algorithms like the Partitioning Around Medoids (PAM) algorithm have two obvious drawbacks which are (1) the algorithm may stop at local optima and (2) sensitive to the initial solution. Therefore, optimal solutions cannot be guaranteed by k-medoids clustering algorithms. In this paper, we present an integer linear programming model for the k-medoids clustering which can be optimally solved by MIP solvers even for mediumsized instances. Experiments on two well-known data sets and a synthesized dataset are carried out under the AMPL/CPLEX environment in a Mac system to compare the performance of our new model to that of the traditional k-medoids. The results show that our new method could find directly the optimal solution, updated best-known solutions of tested problems with optimal solutions, without trapping in locally optimal solutions, and being irrelative to initial solution.