The complexity of non-hierarchical clustering with instance and cluster level constraints

Recent work has looked at extending clustering algorithms with instance level must-link (ML) and cannot-link (CL) background information. Our work introduces δ and ǫ cluster level constraints that influence inter-cluster distances and cluster composition. The addition of background information, though useful at providing better clustering results, raises the important feasibility question: Given a collection of constraints and a set of data, does there exist at least one partition of the data set satisfying all the constraints? We study the complexity of the feasibility problem for each of the above constraints separately and also for combinations of constraints. Our results clearly delineate combinations of constraints for which the feasibility problem is computationally intractable (i.e., NP-complete) from those for which the problem is efficiently solvable (i.e., in the computational class P). We also consider the ML and CL constraints in conjunctive and disjunctive normal forms...

• Type: Journal
• Year: 2007
• Where: DATAMINE
• Authors: Ian Davidson, S. S. Ravi
• Keywords: CL Constraints, DATAMINE 2007, Feasibility Problem, Important Feasibility Question