Fast multiscale clustering and manifold identification

Pattern Recognition

Volumn 39, Issue 10, 2006, Pages 1876-1891

  Kushnir, Dan ^a   Galun, Meirav ^a   Brandt, Achi ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Aggregation; Algebraic multigrid (AMG); Astrophysical models; Data analysis; Graph partitioning; Manifold; Similarity based clustering

Indexed keywords

ALGORITHMS; ASTROPHYSICS; GRAPH THEORY; IDENTIFICATION (CONTROL SYSTEMS); PROCESS CONTROL;

ALGEBRAIC MULTIGRID (AMG); ASTROPHYSICAL MODELS; GRAPH PARTITIONING; MANIFOLD; SIMILARITY-BASED CLUSTERING;

DATA REDUCTION;

EID: 33745422982     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2006.04.007     Document Type: Article

References (34)

1. M. Galun, E. Sharon, R. Basri, A. Brandt, Texture segmentation by multiscale aggregation of filter responses and shape elements, Int. Conf. Comput. Vision (2003) 716-723.
2. E. Sharon, A. Brandt, R. Basri, Fast multiscale image segmentation, Comput. Vision Pattern Recognition (2000) 70-77.
3. A. Brandt, S. McCormick, J. Ruge, Algebraic Multigrid (amg) for Automatic Multigrid Solution with Application to Geodetic Computations, Institute for Computational Studies, POB 1852, Fort Colins, Colorado, 1982.
4. Shi J., and Malik J. Normalized cuts and image segmentation. Trans. Pattern. Anal. Mach. Intell. 22 8 (2000) 888-905
5. Ng Andrew Y., Jordan M., and Weiss Y. On spectral clustering: analysis and an algorithm. Adv. Neural Inform. Process. Syst. 14 (2002)
6. Brandt A., and Ron D. Multigrid solvers and multiscale optimization strategies. In: Cong J., and Shinnerl J.R. (Eds). Multilevel Optimization and VLSICAD (2003), Kluwer, Boston 1-69
7. Duda R.O., Hart P.E., and Stork D.G. Pattern Classification (2001), Wiley, New York
8. Jain A.K., and Dubes R.C. Algorithms for Clustering Data (1988), Prentice-Hall, Englewood Cliffs, NJ
9. Fowlkes C., Belongie S., Chung F., and Malik J. Spectral grouping using the Nystrom method. Trans. Pattern. Anal. Mach. Intell. 26 2 (2004) 214-225
10. Fischer B., Roth V., and Buhmann J.M. Clustering with the connectivity kernel. News Physiol. Sci. 16 (2004)
11. Fischer B., and Buhmann J.M. Bagging for path-based clustering. Trans. Pattern. Anal. Mach. Intell. 25 11 (2003) 1411-1415
12. Blatt M., Wiseman S., and Domany E. Data clustering using a model granular magnet. Neural Comput. 9 8 (1997) 1805-1842
13. Gdalyahu Y., Weinshall D., and Werman M. Self organization in vision: stochastic clustering for image segmentation, perceptual grouping, and image database organization. Trans. Pattern. Anal. Mach. Intell. 23 10 (2001) 1053-1074
14. Guy G., and Medioni G.G. Inference of surfaces, 3D curves, and junctions from sparse, noisy, 3D data. Trans. Pattern. Anal. Mach. Intell. 19 11 (1997) 1265-1277
15. Jollife I.T. Principal Component Analysis (1986), Springer, New York
16. Cox T., and Cox M. Multidimensional Scaling (1994), Chapman & Hall, London
17. Hastie T., and Stuetzle W. Principal curves. J. Am. Statist. Assoc. 84 406 (1989) 502-516
18. LeBlanc M., and Tibshirani R. Adaptive principal surfaces. J. Am. Statist. Assoc. 89 425 (1994) 53-64
19. Stanford D.C., and Raftery A.E. Finding curvilinear features in spatial point patterns: principal curve clustering with noise. Trans. Pattern. Anal. Mach. Intell. 22 6 (2000) 601-609
20. Friedman J.H., and Stuetzle W. Projection pursuit regression. J. Am. Stat. Assoc. 76 376 (1981) 817-823
21. Roweis S., and Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science 290 5500 (2000) 2323-2326
22. Belkin M., and Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15 6 (2003) 1373-1396
23. Tenenbaum J.B., De Silva V., and Langford J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 5500 (2000) 2319-2323
24. de Berg M.T., van Kreveld M.J., Overmars M.H., and Schwarzkopf O. Computational Geometry: Algorithms and Applications (2000), Springer, Heidelberg
25. Y. Goldschmidt, M. Galun, E. Sharon, R. Basri, A. Brandt, Fast multilevel clustering, Technical Report, MCS05-09, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science.
26. Sharon E., Brandt A., and Basri R. Completion energies and scale. Trans. Pattern. Anal. Mach. Intell. 22 10 (2000) 70-77
27. A. Shashua, S. Ullman, Structural saliency: the detection of globally salient structures using a locally connected network, Int. Conf. Comput. Vision (1988) 321-327.
28. Williams L.R., and Jacobs D.W. Stochastic completion fields: a neural model of illusory contour shape and salience. Neural Comput. 9 (1997) 837-858
29. Peebles P. The Large Scale Structure of the Universe (1980), Princeton University Press
30. Starck J.L., and Murtagh F. Astronomical Image and Data Analysis (2002), Springer, New York
31. Hawkins, et al. The 2dF galaxy redshift survey correlation functions peculiar velocities and the matter density of the Universe. Mon. Not. R. Astron. Soc. 346 (2003) 1-19
32. J.A. Peacock, Implications of 2dFGRS results on cosmic structure, AIP Conference Proceedings, vol. 666, 2003, pp. 275-290.
33. Hartigan J.A., and Wong M.A. A k-means clustering algorithm. Appl. Stat. 28 (1979) 100-108
34. Dempster A.P., Laird N.M., and Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. 39 1 (1977) 1-38