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
A spectral method to separate disconnected and nearly-disconnected web graph components
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Spectral clustering and its use in bioinformatics
Journal of Computational and Applied Mathematics
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Eigenvectors and, more generally, singular vectors, have proved to be useful tools for data mining and dimension reduction. Spectral clustering and reordering algorithms have been designed and implemented in many disciplines, and they can be motivated from several different standpoints. Here we give a general, unified derivation from an applied linear algebra perspective. We use a variational approach that has the benefit of (a) naturally introducing an appropriate scaling, (b) allowing for a solution in any desired dimension, and (c) dealing with both the clustering and bi-clustering issues in the same framework. The motivation and analysis is then backed up with examples involving two large data sets from modern, high-throughput, experimental cell biology. Here, the objects of interest are genes and tissue samples, and the experimental data represents gene activity. We show that looking beyond the dominant, or Fiedler, direction reveals important information.