Mixed integer linear programming formulation for K-means clustering problem
Kolos Csaba Ágoston, Marianna E.-Nagy
Abstract
Abstract The minimum sum-of-squares clusering is the most widely used clustering method. The minimum sum-of-squares clustering is usually solved by the heuristic KMEANS algorithm, which converges to a local optimum. A lot of effort has been made to solve such kind of problems, but a mixed integer linear programming formulation (MILP) is still missing. In this paper, we formulate MILP models. The advantage of MILP formulation is that users can extend the original problem with arbitrary linear constraints. We also present numerical results, we solve these models up to sample size of 150.
Topics & Concepts
Cluster analysisInteger programmingMathematical optimizationLinear programmingHeuristicInteger (computer science)k-means clusteringMathematicsComputer scienceBranch and priceStatisticsProgramming languageAdvanced Clustering Algorithms ResearchFacility Location and Emergency ManagementMulti-Criteria Decision Making