Matrix analysis
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmentation Given Partial Grouping Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Semi-supervised graph clustering: a kernel approach
ICML '05 Proceedings of the 22nd international conference on Machine learning
Nonlinear programming: a historical view
ACM SIGMAP Bulletin
Document clustering with prior knowledge
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
The complexity of non-hierarchical clustering with instance and cluster level constraints
Data Mining and Knowledge Discovery
Intractability and clustering with constraints
Proceedings of the 24th international conference on Machine learning
Efficient incremental constrained clustering
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
A tutorial on spectral clustering
Statistics and Computing
Spectral clustering with inconsistent advice
Proceedings of the 25th international conference on Machine learning
Constrained Clustering: Advances in Algorithms, Theory, and Applications
Constrained Clustering: Advances in Algorithms, Theory, and Applications
Identifying and generating easy sets of constraints for clustering
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Flexible constrained spectral clustering
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
IEEE Transactions on Knowledge and Data Engineering
Hi-index | 0.00 |
Constrained clustering has been well-studied for algorithms such as K-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode many constraints is to use spectral clustering, which remains a developing area. In this paper, we propose a flexible framework for constrained spectral clustering. In contrast to some previous efforts that implicitly encode Must-Link (ML) and Cannot-Link (CL) constraints by modifying the graph Laplacian or constraining the underlying eigenspace, we present a more natural and principled formulation, which explicitly encodes the constraints as part of a constrained optimization problem. Our method offers several practical advantages: it can encode the degree of belief in ML and CL constraints; it guarantees to lower-bound how well the given constraints are satisfied using a user-specified threshold; it can be solved deterministically in polynomial time through generalized eigendecomposition. Furthermore, by inheriting the objective function from spectral clustering and encoding the constraints explicitly, much of the existing analysis of unconstrained spectral clustering techniques remains valid for our formulation. We validate the effectiveness of our approach by empirical results on both artificial and real datasets. We also demonstrate an innovative use of encoding large number of constraints: transfer learning via constraints.