Hierarchical eigensolver for transition matrices in spectral methods

Advances in Neural Information Processing Systems

Volumn , Issue , 2005, Pages

  Chennubhotla, Chakra ^a   Jepson, Allan D ^b  

^a UNIVERSITY OF PITTSBURGH SCHOOL OF MEDICINE   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; IMAGE SEGMENTATION; MATLAB;

EIGEN-SOLUTIONS; HIERARCHICAL REPRESENTATION; LARGEST EIGENVALUES; SEGMENTATION ALGORITHMS; SPARSE MATRICES; SPECTRAL METHODS; STOCHASTIC MATRICES; TRANSITION MATRICES;

MATRIX ALGEBRA;

EID: 84898993973     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. D. Achlioptas and F. McSherry. Fast Computation of Low-Rank Approximations. STOC, 2001.
2. D. Achlioptas et al Sampling Techniques for Kernel Methods. NIPS, 2001.
3. S. Barnard and H. Simon Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems. PPSC, 627-632.
4. M. Belkin et al Laplacian Eigenmaps and Spectral Techniques for Embedding. NIPS, 2001.
5. M. Brand et al A unifying theorem for spectral embedding and clustering. AI & STATS, 2002.
6. C. Chennubhotla. Spectral Methods for Multi-scale Feature Extraction and Spectral Clustering. http://www.cs.toronto.edu/chakra/thesis.pdf Ph.D Thesis, Department of Computer Science, University of Toronto, Canada, 2004.
7. C. Chennubhotla and A. Jepson. Half-Lives of EigenFlows for Spectral Clustering. NIPS, 2002.
8. F. Estrada, A. Jepson and C. Chennubhotla. Spectral Embedding and Min-Cut for Image Segmentation. Manuscript Under Review, 2004.
9. C. Fowlkes et al Efficient spatiotemporal grouping using the Nystrom method. CVPR, 2001.
10. S. Belongie et al Spectral Partitioning with Indefinite Kernels using Nystrom app. ECCV, 2002.
11. A. Frieze et al Fast Monte-Carlo Algorithms for finding low-rank approximations. FOCS, 1998.
12. Y. Koren et al ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs IEEE Symp. on InfoVis 2002, pp. 137-144.
13. R. B. Lehoucq, D. C. Sorensen and C. Yang. ARPACK User Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. SIAM 1998.
14. J. J. Lin. Reduced Rank Approximations of Transition Matrices. AI & STATS, 2002.
15. L. Lova'sz. Random Walks on Graphs: A Survey Combinatorics, 1996, 353-398.
16. G. J. McLachlan et al Mixture Models: Inference and Applications to Clustering. 1988.
17. M. Meila and J. Shi. A random walks view of spectral segmentation. AI & STATS, 2001.
18. A. Ng, M. Jordan and Y.Weiss. On Spectral Clustering: Analysis and an algorithm NIPS, 2001.
19. A. Pothen Graph partitioning algorithms with applications to scientific computing. Parallel Numerical Algorithms, D. E. Keyes et al (eds.), Kluwer Academic Press, 1996.
20. G. L. Scott et al Feature grouping by relocalization of eigenvectors of the proximity matrix. BMVC, pg. 103-108, 1990.
21. E. Sharon et al Fast Multiscale Image Segmentation CVPR, 1:70-77, 2000.
22. J. Shi and J. Malik. Normalized cuts and image segmentation. PAMI, August, 2000.
23. H. Simon et al Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications SIAM J. of Sci. Comp. 21(6):2257-2274, 2000.
24. N. Tishby et al Data clustering by Markovian Relaxation NIPS, 2001.
25. C. Williams et al Using the Nystrom method to speed up the kernel machines. NIPS, 2001.