A loss function approach to model selection in nonlinear principal components

Neural Networks

Volumn 12, Issue 2, 1999, Pages 339-345

  Webb, Andrew R ^a  

^a DEFENCE SCIENCE AND TECHNOLOGY LABORATORY   (United Kingdom)

Author keywords

Dimension reduction; Homogeneity analysis; Nonlinear feature extraction; Nonlinear principal components analysis; Principal curves; Radial basis functions

Indexed keywords

ALGORITHMS; FEATURE EXTRACTION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; STATISTICAL METHODS;

HOMOGENEITY ANALYSIS; NONLINEAR PRINCIPAL COMPONENTS ANALYSIS; RADIAL BASIS FUNCTIONS;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; VALIDATION PROCESS; VARIANCE;

EID: 0033104438     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(98)00114-2     Document Type: Article

References (17)

1. Broomhead, D. S., & Lowe, D. (1988). Multi-variable functional interpolation and adaptive networks. Complex Systems, 2 (3), 269-303.
2. Gifi, A. (1990). Nonlinear multivariate analysis. Chichester: Wiley.
3. Green, P. J., & Silverman, B. W. (1994). Nonlinear regression and generalized linear models. A roughness penalty approach. Monographs on Statistics and Applied Probability, Number 58. London: Chapman and Hall.
4. Hand, D. J., Daley, F., Lunn, A. D., McConway, K. J., & Ostrowski, E. (1994). A handbook of small data sets. London: Chapman and Hall.
5. Hartigan, J. A., & Wong, M. A. (1979). A k-means clustering algorithm. Applied Statistics, 28, 100-110.
6. Hastie, T., & Stuetzle, W. (1989). Principal curves. Journal of the American Statistical Association, 84, 502-516.
7. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417-441. (also pp. 498-520).
8. Karhunen, J., & Joutsensalo, J. (1994). Representation and separation of signals using nonlinear pea type learning. Neural Networks, 7 (1), 113-127.
9. Kramer, M. A. (1991). Nonlinear principal component analysis using auto-associative neural networks. American Institute of Chemical Engineers Journal, 37 (2), 233-243.
10. LeBlanc, M., & Tibshirani, R. (1994). Adaptive principal surfaces. Journal of the American Statistical Association, 89, 53-664.
11. Lowe, D. (1995). On the use of nonlocal and non positive definite basis functions in radial basis function networks. Proceedings of the IEE International Conference on Artificial Neural Networks, Cambridge.
12. Mertens, B., Fearn, T., & Thompson, M. (1995). The efficient cross-validation of principal components applied to principal component regression. Statistics and Computing, 5 (3), 227-235.
13. Nakagawa, S., Ono, Y., & Hirata, Y. (1991). Dimensionality reduction of dynamical patterns using a neural network. In B. H. Juang, S. Y. Kung, & C. A. Kamm (Eds.), Proceedings of the 1991 IEEE Workshop, Neural Networks for Signal Processing (pp. 256-265). Princeton, NJ: IEEE.
14. Pearson, K. (1901). On lines and planes of closest fit. Philosophical Magazine, 6, 559-572.
15. Tibshirani, R. (1992). Principal curves revisited. Statistics and Computing, 2 (4), 183-190.
16. Usui, S., Nakauchi, S., & Nakano, M. (1990). Reconstruction of Munsell color space by a five-layered neural network. In IJCNN International Joint Conference on Neural Networks, (Vol. II, pp. 515-520), San Diego, CA: IEEE.
17. Webb, A. R. (1996). An approach to nonlinear principal components analysis using radially-symmetric kernel functions. Statistics and Computing, 6 (2), 159-168.