Non-linear independent component analysis with diffusion maps

Applied and Computational Harmonic Analysis

Volumn 25, Issue 2, 2008, Pages 226-239

  Singer, Amit ^a   Coifman, Ronald R ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ESTIMATION; FINANCIAL DATA PROCESSING; MAPS; MULTIVARIANT ANALYSIS; PRINCIPAL COMPONENT ANALYSIS; SEMICONDUCTOR DOPING;

ANISOTROPIC DIFFUSION (AD); DATA MANIFOLDS; DISTORTION (DEFORMATION); EMPIRICAL DATA; INDEPENDENT COMPONENTS; INDEPENDENT VARIABLES; JACOBIAN; LAPLACIAN; LOCAL PRINCIPAL COMPONENT ANALYSIS; NON LINEAR TRANSFORMATIONS; NON-LINEAR; PARAMETERIZATIONS; SECOND ORDER APPROXIMATION;

INDEPENDENT COMPONENT ANALYSIS;

EID: 48349109325     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2007.11.001     Document Type: Article

References (19)

1. Roweis S.T., and Saul L.K. Nonlinear dimensionality reduction by locally linear embedding. Science 290 5500 (2000) 2323-2326
2. Donoho D.L., and Grimes C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc. Nat. Acad. Sci. 100 10 (2003) 5591-5596
3. Belkin M., and Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15 (2003) 1373-1396
4. Coifman R.R., and Lafon S. Diffusion maps. Appl. Comput. Harmon. Anal. 21 1 (2006) 5-30
5. Singer A. Spectral independent component analysis. Appl. Comput. Harmon. Anal. 21 1 (2006) 135-144
6. Hyvärinen A., and Pajunen P. Non linear independent component analysis: Existence and uniqueness results. Neural Networks 12 3 (1999) 429-439
7. m: A technique applied to recovering articulation from acoustics. Speech Commun. 49 (2007) 361-383
8. Jutten C., and Karhunen J. Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures. Int. J. Neural Systems 14 5 (2004) 267-292
9. Almeida L. Nonlinear Source Separation. Synthesis Lectures on Signal Processing (2005), Morgan & Claypool Publishers 114 pp
10. A. Singer, R. Erban, I. Kevrekidis, R.R. Coifman, Detecting the slow manifold by anisotropic diffusion maps, preprint
11. S. Lafon, Diffusion maps and geometric harmonics, Ph.D. dissertation, Yale University, 2004
12. Nadler B., Lafon S., Coifman R.R., and Kevrekidis I. Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators. In: Weiss Y., Schölkopf B., and Platt J. (Eds). Advances in Neural Information Processing Systems vol. 18 (2006), MIT Press, Cambridge, MA 955-962
13. Nadler B., Lafon S., Coifman R.R., and Kevrekidis I.G. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Appl. Comput. Harmon. Anal. 21 1 (2006) 113-127
14. Zelnik-Manor L., and Perona P. Self-tuning spectral clustering. In: Saul L.K., Weiss Y., and Bottou L. (Eds). Advances in Neural Information Processing Systems 17 (NIPS'04) (2005), MIT Press, Cambridge, MA 1601-1608
15. Basu S., and Bresler Y. Feasibility of tomography with unknown view angles. IEEE Trans. Image Process. 9 6 (2000) 1107-1122
16. R.R. Coifman, Y. Shkolnisky, F.J. Sigworth, A. Singer, Graph Laplacian tomography from unknown random projections, IEEE Trans. Image Process., in press
17. A. Jansen, P. Niyogi, Intrinsic Fourier analysis on the manifold of speech sounds, in: Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'2006), 2006
18. A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, Wiley, New York
19. Belkin M., and Niyogi P. Towards a theoretical foundation for Laplacian-based manifold methods. In: Auer P., and Meir R. (Eds). Proc. 18th Conf. Learning Theory (COLT). Lecture Notes Comput. Sci. vol. 3559 (2005), Springer-Verlag, Berlin 486-500