Automatic configuration of spectral dimensionality reduction methods

Pattern Recognition Letters

Volumn 31, Issue 12, 2010, Pages 1720-1727

  Lewandowski, Michał ^a   Makris, Dimitrios ^a   Nebel, Jean Christophe ^a  

^a KINGSTON UNIVERSITY   (United Kingdom)

Author keywords

Dimensionality reduction; Isomap; Laplacian Eigenmaps; Locally Linear Embedding; Mutual information; Radial Basis Function network

Indexed keywords

AUTOMATIC CONFIGURATION; CLUSTER ALGORITHMS; DIMENSIONALITY REDUCTION; DIMENSIONALITY REDUCTION METHOD; LAPLACIAN EIGENMAPS; LEARNING PROCESS; LOCALLY LINEAR EMBEDDING; MUTUAL INFORMATIONS; REAL DATA SETS;

ATTITUDE CONTROL; GRAPH THEORY; LAPLACE TRANSFORMS; LEARNING ALGORITHMS;

RADIAL BASIS FUNCTION NETWORKS;

EID: 77955559751     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patrec.2010.05.025     Document Type: Article

References (43)

1. C. Aggarwal, A. Hinneburg, and D. Keim On the surprising behavior of distance metrics in high dimensional spaces Lect. Notes Comput. Sci. 1973 2001 420 434
2. M. Belkin, and P. Niyogi Laplacian eigenmaps and spectral techniques for embedding and clustering Adv. Neural Inform. Process. Systems 14 2001 585 591
3. C. Bishop, M. Svensén, and C. Williams GTM: The generative topographic mapping Neural Comput. 10 1 1998 215 234
4. F. Camastra Data dimensionality estimation methods: A survey Pattern Recognition 36 12 2003 2945 2954
5. F. Camastra, and A. Vinciarelli Intrinsic dimension estimation of data: An approach based on Grassberger-Procacciaś algorithm Neural Process. Lett. 14 1 2001 27 34
6. S. Chen, C. Cowan, and P. Grant Orthogonal least squares learning algorithm for radial basis function networks IEEE Trans. Neural Networks 2 2 1991 302 309
7. H. Choi, and S. Choi Kernel isomap IET Electron. Lett. 40 25 2004 1612 1613
8. J. Costa, and A. Hero Geodesic entropic graphs for dimension and entropy estimation in manifold learning IEEE Trans. Signal Process. 52 8 2004 2210 2221
9. T.M. Cover, and J. Thomas Elements of Information Theory 1991 Wiley
10. D. De Ridder, O. Kouropteva, O. Okun, M. Pietikainen, and R. Duin Supervised locally linear embedding Lect. Notes Comput. Sci. 2714 2003 333 341
11. V. De Silva, and J. Tenenbaum Global versus local methods in nonlinear dimensionality reduction Adv. Neural Inform. Process. Systems 15 2003 705 712
12. Dongen, S.; 2000. Graph Clustering by Flow Simulation, Ph.D. Thesis, University of Utrecht, The Netherlands.
13. D. Donoho, and C. Grimes Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data Proc. Natl. Acad. Sci. 100 10 2003 5591 5596
14. A. Elgammal, and C. Lee Nonlinear manifold learning for dynamic shape and dynamic appearance Comput. Vision and Image Understanding 106 1 2007 31 46
15. Fukunaga, K.; 1982. Intrinsic dimensionality extraction. In: Classification, Pattern Recognition and Reduction of Dimensionality, pp. 347-362.
16. K. Fukunaga, and D.R. Olsen An algorithm for finding intrinsic dimensionality of data IEEE Trans. Comput. C-20 2 1971 176 183
17. Goldberg, Y.; Ritov, Y.; 2008. LDR-LLE: LLE with low-dimensional neighborhood representation. In: ISVC'08: Proc. 4th Internat. Symposium on Advances in Visual Computing, Part II, pp. 43-54.
18. Y. Goldberg, and Y. Ritov Local procrustes for manifold embedding: A measure of embedding quality and embedding algorithms Machine Learning 77 1 2009 1 25
19. X. He, and P. Niyogi Locality preserving projections Adv. Neural Inform. Process. Systems 16 2004 153 160
20. He, X.; Ma, W.; Zhang, H.; 2004. Learning an image manifold for retrieval. In: Proc. ACM Multimedia, pp. 17-23.
21. He, X.; Cai, D.; Yan, S.; Zhang, H.; 2005. Neighborhood preserving embedding. In: Proc. IEEE Internat. Conf. on Computer Vision, vol. 2, pp. 1208-1213.
22. T. Ho Nearest neighbors in random subspaces Lect. Notes Comput. Sci. 1451 1998 640 648
23. Kanungo, T.; Mount, D.; Netanyahu, N.; Piatko, C.; Silverman, R.; Wu, A.; 2002. A local search approximation algorithm for k-means clustering. In: Proc. 18th Annual Symposium on Computational Geometry, pp. 10-18.
24. R. Karbauskait, O. Kurasova, and G. Dzemyda Selection of the number of neighbours of each data point for the locally linear embedding algorithm Inform. Technol. Control 36 4 2007 359 364
25. B. Kegl Intrinsic dimension estimation using packing numbers Adv. Neural Inform. Process. Systems 15 2003 681 688
26. E. Kokiopoulou, and Y. Saad Orthogonal neighborhood preserving projections: A projection-based dimensionality reduction technique IEEE Trans. Pattern Anal. Machine Intell. 29 12 2007 2143 2156
27. Kouropteva, O.; Okun, O.; Pietikainen, M.; 2002. Selection of the optimal parameter value for the locally linear embedding algorithm. In: Proc. 1st Internat. Conf. on Fuzzy Systems and Knowledge Discovery, Singapore, pp. 359-363.
28. A. Kraskov, H. Stoegbauer, and P. Grassberger Estimating mutual information Phys. Rev. E - Statist. Nonlinear Soft Matter Phys. 69 6 2004 66138
29. N. Lawrence Gaussian process latent variable models for visualisation of high dimensional data Adv. Neural Inform. Process. Systems 2004 16
30. LeCun, Y.; 2000. MNIST handwritten digits dataset (http://yann.lecun.com/ exdb/mnist/index.html ) (last accessed 30.10.09).
31. E. Levina, and P. Bickel Maximum likelihood estimation of intrinsic dimension Adv. Neural Inform. Process. Systems 17 2005 777 784
32. Lewandowski, M.; Makris, D.; Nebel, J.-C.; 2009. Automatic configuration of spectral dimensionality reduction methods for 3D human pose estimation. In: Visual Surveillance.
33. T. Poggio, F. Girosi, and C. MIT Networks for approximation and learning Proc. IEEE 78 9 1990 1481 1497
34. S. Roweis, and L. Saul Nonlinear dimensionality reduction by locally linear embedding Science 290 5500 2000 2323 2326
35. Samaria, F.; Harter, A.; 1994. Parameterisation of a stochastic model for human face identification. In: Workshop on Applications of Computer Vision (http://www.cs.toronto.edu/∼roweis/data.html ) (last accessed 30.10.09).
36. O. Samko, A. Marshall, and P. Rosin Selection of the optimal parameter value for the Isomap algorithm Pattern Recognition Lett. 27 9 2006 968 979
37. J. Tenenbaum, V. Silva, and J. Langford A global geometric framework for nonlinear dimensionality reduction Science 290 5500 2000 2319 2323
38. Q. Wang, and J. Li Combining local and global information for nonlinear dimensionality reduction Neurocomputing 72 10-12 2009 2235 2241
39. L. Xu, A. Krzyzak, and E. Oja Rival penalized competitive learning for clustering analysis, RBFnet, and curve detection IEEE Trans. Neural Networks 4 4 1993 636 649
40. M. Yang Discriminant isometric mapping for face recognition Lect. Notes Comput. Sci. 2626 2003 470 480
41. J. Yin, D. Hu, and Z. Zhou Growing locally linear embedding for manifold learning J. Pattern Recognition Res. 2 1 2008 1 16
42. Z. Zhang, and J. Wang Mlle: Modified locally linear embedding using multiple weights Adv. Neural Inform. Process. Systems 19 2007 1593 1600
43. F. Zheng, N. Chen, and L. Li Semi-supervised Laplacian eigenmaps for dimensionality reduction Wavelet Anal. Pattern Recognition 2 2008 843 849