Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions

Applied and Computational Harmonic Analysis - Tập 21 - Trang 31-52 - 2006
Ronald R. Coifman1, Stéphane Lafon1
1Applied Mathematics Department, Yale University, New Haven, CT 06510, USA

Tài liệu tham khảo

Abramowitz, 1965 Aronszajn, 1950, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68, 10.1090/S0002-9947-1950-0051437-7 Y. Bengio, J.-F. Paiement, P. Vincent, Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering, Technical report 1238, Université de Montréal, 2003 M. Belkin, P. Nyoigi, V. Sindhwani, On manifold regularization, in: Proc. 10th Int. Workshop on Artificial Intelligence and Statistics, Society for Artificial Intelligence and Statistics, pp. 17–24 Wackernagel, 2003 Schoenberg, 1938, Metric spaces and completely monotone functions, Ann. of Math. (2), 39, 811, 10.2307/1968466 R.R. Coifman, S. Lafon, Diffusion maps, in preparation Folland, 1976 C. Fowlkes, S. Belongie, J. Malik, Efficient spatiotemporal grouping using the Nyström method, IEEE Comput. Vision Pattern Recogn, December 2001 W.H. Press, S.A. Teulkosky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C, Cambridge Univ. Press, New York, chap. 18.1 Slepian, 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty I, Bell System Tech. J., 40, 43, 10.1002/j.1538-7305.1961.tb03976.x Slepian, 1964, Prolate spheroidal wave functions, Fourier analysis and uncertainty IV: Extensions to many dimensions; generalized prolate spheroidal wave functions, Bell System Tech. J., 43, 3009, 10.1002/j.1538-7305.1964.tb01037.x Williams, 2001, Using the Nyström method to speed up kernel machines, Neural Inf. Process. Systems, 13, 682