Journal of Algorithms
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Accelerating exact k-means algorithms with geometric reasoning
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
On the Complexity of Mining Quantitative Association Rules
Data Mining and Knowledge Discovery
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constrained K-means Clustering with Background Knowledge
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Semi-supervised Clustering by Seeding
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Refining Initial Points for K-Means Clustering
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Clustering with Instance-level Constraints
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Intelligent clustering with instance-level constraints
Intelligent clustering with instance-level constraints
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A probabilistic framework for semi-supervised clustering
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Integrating constraints and metric learning in semi-supervised clustering
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Agglomerative hierarchical clustering with constraints: theoretical and empirical results
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
Efficient incremental constrained clustering
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Data Mining and Knowledge Discovery
A principled and flexible framework for finding alternative clusterings
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
A Probabilistic Approach for Constrained Clustering with Topological Map
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
Statistical Relational Learning with Formal Ontologies
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Knowledge driven dimension reduction for clustering
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Integer linear programming models for constrained clustering
DS'10 Proceedings of the 13th international conference on Discovery science
Constraint selection for semi-supervised topological clustering
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part I
Two approaches to understanding when constraints help clustering
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
On constrained spectral clustering and its applications
Data Mining and Knowledge Discovery
Machine Learning
| Hi-index | 0.00 |
Recent work has looked at extending clustering algorithms with instance level must-link (ML) and cannot-link (CL) background information. Our work introduces 驴 and 驴 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 (CNF and DNF respectively). We show that for ML constraints, the feasibility problem is intractable for CNF but efficiently solvable for DNF. Unfortunately, for CL constraints, the feasibility problem is intractable for both CNF and DNF. This effectively means that CL-constraints in a non-trivial form cannot be efficiently incorporated into clustering algorithms. To overcome this, we introduce the notion of a choice-set of constraints and prove that the feasibility problem for choice-sets is efficiently solvable for both ML and CL constraints. We also present empirical results which indicate that the feasibility problem occurs extensively in real world problems.