Principal surfaces from unsupervised kernel regression

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 27, Issue 9, 2005, Pages 1379-1391

  Meinicke, Peter ^a   Klanke, Stefan ^b   Memisevic, Roland ^c   Ritter, Helge ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b BIELEFELD UNIVERSITY   (Germany)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Density estimation; Dimensionality reduction; Kernel methods; Model selection; Principal curves; Principal surfaces

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; MULTILAYER NEURAL NETWORKS; OPTIMIZATION; PARAMETER ESTIMATION; PRINCIPAL COMPONENT ANALYSIS; RADIAL BASIS FUNCTION NETWORKS; REGRESSION ANALYSIS; VECTORS;

DENSITY ESTIMATION; DIMENSIONALITY REDUCTION; KERNEL METHODS; MODEL SELECTION; PRINCIPAL CURVES; PRINCIPAL SURFACES;

LEARNING SYSTEMS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; EVALUATION; INFORMATION RETRIEVAL; METHODOLOGY; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED; PRINCIPAL COMPONENT ANALYSIS;

EID: 25844496193     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2005.183     Document Type: Article

References (30)

1. P. Meinicke, "Unsupervised Learning in a Generalized Regression Framework," PhD dissertation, Universität Bielefeld, 2000.
2. T. Hastie, "Principal Curves and Surfaces," PhD dissertation, Stanford Univ., 1984.
3. B. Kégl, A. Krzyzak, T. Linder, and K. Zeger, "Learning and Design of Principal Curves," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 3, pp. 281-297, Mar. 2000.
4. M. LeBlanc and R. Tibshirani, "Adaptive Principal Surfaces," J. Am. Statistical Assoc., vol. 89, pp. 53-64, 1994.
5. A.J. Smola, S. Mika, B. Schölkopf, and R.C. Williamson, "Regularized Principal Manifolds," J. Machine Learning Research, vol. 1, pp. 179-209, 2001.
6. K. Chang and J. Ghosh, "A Unified Model for Probabilistic Principal Surfaces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 1, pp. 22-41, Jan. 2001.
7. C.M. Bishop, M. Svensen, and C.K.I. Williams, "GTM: The Generative Topographic Mapping," Neural Computation, vol. 10, no. 1, pp. 215-234, 1998.
8. T. Kohonen, Self-Organizing Maps. Springer, 1995.
9. H. Ritter, T. Martinetz, and K. Schulten, Neural Computation and Self-Organizing Maps. Addison Wesley, 1992.
10. J. Walter and H. Ritter, "Rapid Learning with Parametrized Self-Organizing Maps," Neurocomputing, vol. 12, pp. 131-153, 1996.
11. C.M. Bishop, M. Svensén, and C.K.I. Williams, "Developments of the Generative Topographic Mapping," Neurocomputing, vol. 21, pp. 203-224, 1998.
12. B. Schölkopf and A.J. Smola, Learning with Kernels. MIT Press, 2002.
13. E.A. Nadaraya, "On Estimating Regression," Theory of Probability and Its Application, vol. 10, pp. 186-190, 1964.
14. G. Watson, "Smooth Regression Analysis," Sankhya Series A, vol. 26, pp. 359-372, 1964.
15. D.W. Scott, Multivariate Density Estimation. Wiley, 1992.
16. T. Hastie, R. Tibshirani, and J.H. Friedman, The Elements of Statistical Learning. Springer-Verlag, 2001.
17. S. Sandilya and S.R. Kulkarni, "Principal Curves with Bounded Turn," IEEE Trans. Information Theory, vol. 48, pp. 2789-2793, 2002.
18. S. Roweis and L. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, pp. 2323-2326, 2000.
19. J.B. Tenenbaum, V. de Silva, and J.C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, pp. 2319-2323, 2000.
20. M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," Neural Computation, vol. 15, no. 6, pp. 1373-1396, June 2003.
21. H. Reiner, Handbook of Global Optimization. Dordrecht: Kluwer Academic Publishers, 1995.
22. G.H. Bakir, J. Weston, and B. Schölkopf, "Learning to Find Pre-Images," Advances in Neural Information Processing Systems, 2003.
23. J.T. Kwok and I.W. Tsang, "Finding the Pre Images in Kernel Principal Component Analysis," Proc. Sixth Ann. Workshop Kernel Machines, 2002.
24. J. Weston, O. Chapelle, A. Elisseeff, B. Schölkopf, and V. Vapnik, "Kernel Dependency Estimation," Advances in Neural Information Processing Systems 15, 2003.
25. B. Silverman, Density Estimation for Statistics and Data Analysis. London-New York: Chapman and Hall, 1986.
26. J.C. Lagarias, J.A. Reeds, M.H. Wright, and P.E. Wright, "Convergence Properties of the Nelder-Mead Simplex Algorithm in Low Dimensions," SIAM J. Optimization, vol. 9, pp. 112-147, 1998.
27. M. Riedmiller and H. Braun, "A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm," Proc. IEEE Int'l Conf. Neural Networks, pp. 586-591, 1993.
28. J.W. Sammon, Jr., "A Non-Linear Mapping for Data Structure Analysis," IEEE Trans. Computers, vol. 18, pp. 401-409, 1969.
29. B. Schölkopf, A.J. Smola, and K.-R. Müller, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem," Neural Computation, vol. 10, pp. 1299-1319, 1998.
30. Y. Bengio, J.-F.P.O. Delalleau, P. Vincent, and M. Ouimet, "Learning Eigenfunctions Links Spectral Embedding and Kernel PCA," Neural Computation, vol. 16, pp. 2197-2219, 2004.