Matrix analysis
An improved spectral graph partitioning algorithm for mapping parallel computations
SIAM Journal on Scientific Computing
Spectral partitioning: the more eigenvectors, the better
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
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
On clusterings-good, bad and spectral
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A clustering coefficient for weighted networks, with application to gene expression data
AI Communications - Network Analysis in Natural Sciences and Engineering
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
TRACEMIN-Fiedler: a parallel algorithm for computing the Fiedler vector
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Self-adjust local connectivity analysis for spectral clustering
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
Computer Science Review
A Laplacian spectral method in phase I analysis of profiles
Applied Stochastic Models in Business and Industry
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Random walk distances in data clustering and applications
Advances in Data Analysis and Classification
From biological to social networks: Link prediction based on multi-way spectral clustering
Data & Knowledge Engineering
| Hi-index | 7.29 |
We formulate a discrete optimization problem that leads to a simple and informative derivation of a widely used class of spectral clustering algorithms. Regarding the algorithms as attempting to bi-partition a weighted graph with N vertices, our derivation indicates that they are inherently tuned to tolerate all partitions into two non-empty sets, independently of the cardinality of the two sets. This approach also helps to explain the difference in behaviour observed between methods based on the unnormalized and normalized graph Laplacian. We also give a direct explanation of why Laplacian eigenvectors beyond the Fiedler vector may contain fine-detail information of relevance to clustering. We show numerical results on synthetic data to support the analysis. Further, we provide examples where normalized and unnormalized spectral clustering is applied to microarray data-here the graph summarizes similarity of gene activity across different tissue samples, and accurate clustering of samples is a key task in bioinformatics.