Bayesian classification (AutoClass): theory and results
Advances in knowledge discovery and data mining
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Co-clustering documents and words using bipartite spectral graph partitioning
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Contour and Texture Analysis for Image Segmentation
International Journal of Computer Vision
A Min-max Cut Algorithm for Graph Partitioning and Data Clustering
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Multiclass Spectral Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Segmentation Given Partial Grouping Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
Kernel k-means: spectral clustering and normalized cuts
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Linearized cluster assignment via spectral ordering
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Spectral Segmentation with Multiscale Graph Decomposition
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Resampling Method for Unsupervised Estimation of Cluster Validity
Neural Computation
Spectral clustering of biological sequence data
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
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Spectral clustering is a completely different algorithm from other existing clustering algorithms in that it relies on a linear algebraic approach including spectral decomposition. Normalized Cuts is a representative algorithm of spectral clustering. It incorporates a criterion for deciding the number k of clusters to partition. This paper shows that the criterion is not appropriate for deciding k. We showed this by proving that the optimal bipartition (that is, when k=2) becomes the optimal clustering. Namely, based on the criterion, the evaluation becomes better when k is small. We also show that the criterion is inappropriate for comparing approximate solutions with various k. Especially we prove that a bipartition which surpasses the best given approximate solution can be constructed from within the time complexity at most , where is the number of clusters contained in . Based on these two reasons, the Normalized Cuts Criterion is not appropriate for deciding k. An alternative criterion is necessary.