A spectral algorithm for envelope reduction of sparse matrices
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Min-max Cut Algorithm for Graph Partitioning and Data Clustering
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Unsupervised Learning: Self-aggregation in Scaled Principal Component Space
PKDD '02 Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery
Cluster merging and splitting in hierarchical clustering algorithms
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
Multiclass Spectral Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Spectral clustering for multi-type relational data
ICML '06 Proceedings of the 23rd international conference on Machine learning
Computers and Operations Research
Nestedness and segmented nestedness
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Inappropriateness of the criterion of k-way normalized cuts for deciding the number of clusters
Pattern Recognition Letters
Graph nodes clustering with the sigmoid commute-time kernel: A comparative study
Data & Knowledge Engineering
PCA-Guided k-Means with Variable Weighting and Its Application to Document Clustering
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Graph nodes clustering based on the commute-time kernel
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Fuzzy PCA-guided robust k-means clustering
IEEE Transactions on Fuzzy Systems
Knowledge and Information Systems
Clustered Nyström method for large scale manifold learning and dimension reduction
IEEE Transactions on Neural Networks
Computer Science Review
Hierarchical kernel spectral clustering
Neural Networks
Left-Right oscillate algorithm for community detection used in e-learning system
CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
Fuzzy Cluster Validation Based on Fuzzy PCA-Guided Procedure
International Journal of Fuzzy System Applications
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Spectral clustering uses eigenvectors of the Laplacian of the similarity matrix. They are most conveniently applied to 2-way clustering problems. When applying to multi-way clustering, either the 2-way spectral clustering is recursively applied or an embedding to spectral space is done and some other methods are used to cluster the points. Here we propose and study a K-way cluster assignment method. The method transforms the problem to find valleys and peaks of a 1-D quantity called cluster crossing, which measures the symmetric cluster overlap across a cut point along a linear ordering of the data points. The method can either determine K clusters in one shot or recursively split a current cluster into several smaller ones. We show that a linear ordering based on a distance sensitive objective has a continuous solution which is the eigenvector of the Laplacian, showing the close relationship between clustering and ordering. The method relies on the connectivity matrix constructed as the truncated spectral expansion of the similarity matrix, useful for revealing cluster structure. The method is applied to newsgroups to illustrate introduced concepts; experiments show it outperforms the recursive 2-way clustering and the standard K-means clustering.