Data smoothing regularization, multi-sets-learning, and problem solving strategies

Neural Networks

Volumn 16, Issue 5-6, 2003, Pages 817-825

  Xu, Lei ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Data smoothing; Gaussian mixture; Multiple objects; Problem solving; Tikhonov regularization

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPETITION; INFORMATION MANAGEMENT; LEARNING SYSTEMS; PROBLEM SOLVING;

DATA SMOOTHING;

NEURAL NETWORKS;

ADAPTATION; ALGORITHM; ANALYTIC METHOD; ANALYTICAL ERROR; CONFERENCE PAPER; DATA ANALYSIS; GEOMETRY; INFORMATION PROCESSING; LEARNING; MATHEMATICAL ANALYSIS; PARAMETER; PRIORITY JOURNAL; PROBABILITY; PROBLEM SOLVING; PROCESS MODEL; RANDOMIZATION; SAMPLE SIZE; STRUCTURE ANALYSIS;

EID: 0038355082     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(03)00119-9     Document Type: Conference Paper

References (34)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 19:1974;714-723.
2. Ballard D.H. Generalizing the Hough transform to detecting arbitary shapes. Pattern Recognition. 13:(2):1981;111-122.
3. Bishop C.M. Training with noise is equivalent to Tikhonov regularization. Neural Computation. 7:1995;108-116.
4. Dempster A.P., Laird N.M., Rubin D.B. Maximum-likelihood from incomplete data via the EM algorithm. Journal of Royal Statistical Society. B39:1977;1-38.
5. Devroye L., Györfi L., Lugosi G. A probability theory of pattern recognition. 1996;Springer, Berlin.
6. Fischler M.A., Bolles R.C. Random sample consensus: A paradigm for modeling fitting with applications to image analysis and automated cartography. Communications of ACM. 24:1981;381-395.
7. Girosi F., Jones M., Poggio T. Regularization theory and neural architectures. Neural Computation. 7:1995;219-269.
8. Hough, P. V. C (1962). Method and means for recognizing complex patterns. US Patent No. 3069654, December 18.
9. Hu X.L., Xu L. A comparative study of several cluster number selection criteria. Proceedings of IDEAL03, March 21-23, Hong Kong. 2003;. in press.
10. Redner R.A., Walker H.F. Mixture densities, maximum likelihood, and the EM algorithm. SIAM Review. 26:1984;195-239.
11. Rissanen J. Hypothesis selection and testing by the MDL principle. Computer Journal. 42:(4):1999;260-269.
12. Schwarz G. Estimating the dimension of a model. Annals of Statistics. 6:1978;461-464.
13. Tikhonov A.N., Arsenin V.Y. Solutions of ill-posed problems. 1977;Winston, Baltimore, MD.
14. Xu L. Multisets modeling learning: An unified theory for supervised and unsupervised learning. Proceedings of IEEE ICNN94, June 26-July 2, 1994, Orlando, FL. I:1994;315-320.
15. Xu L. Bayesian-Kullback coupled Ying-Yang machines: Unified learnings and new results on vector quantization. Proceedings of ICONIP95, Oct 30-Nov 3, 1995, Beijing, China. 1995;977-988.
16. Xu L. A unified learning framework: Multisets modeling learning. Proceedings of the 1995 World Congress on Neural Networks, July 17-21, 1995, Washington, DC. I:1995;35-42.
17. Xu L. Bayesian-Kullback Ying-Yang learning scheme: Reviews and new results. Proceedings of ICONIP96, Sept 24-27, 1996, Hong Kong. 1:1996;59-67.
18. Xu L. A unified learning scheme: Bayesian-Kullback Ying-Yang machine. Advances in Neural Information Processing Systems. 8:1996;444-450.
19. Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach: (I) Unsupervised and semi-unsupervised learning. Amari S., Kassabov N. Brain-like computing and intelligent information systems. 1997;241-274 Springer, Berlin.
20. Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach: (II) From unsupervised learning to supervised learning and temporal modeling. Leung D.Y. Theoretical aspects of neural computation: A multidisciplinary perspective. 1997;25-42 Springer, Berlin.
21. Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach: (II): Models and algorithms for dependence reduction, data dimension reduction, ICA and supervised learning. Leung D.Y. Theoretical aspects of neural computation: A multidisciplinary perspective. 1997;Springer, Berlin.
22. Xu L. Bayesian Ying-Yang machine, clustering and number of clusters. Pattern Recognition Letters. 18:(11):1997;1167-1178.
23. Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach (VII): Data smoothing. Proceedings of ICONIP'98, Oct 21-23, 1998, Kitakyushu, Japan. 1:1998;243-248.
24. Xu L. BKYY three layer net learning, EM-like al-gorithm, and selection criterion for hidden unit number. Proceedings of ICONIP'98, Oct 21-23, 1998, Kitakyushu, Japan. 2:1998;631-634.
25. Xu L. Rival penalized competitive learning, finite mixture, and multisets clustering. Proceedings of IJCNN98, May 5-9, 1998, Anchorage, Alaska. II:1998;2525-2530.
26. Xu L. BYY data smoothing based learning on a small size of samples. Proceedings of IJCNN'99, Washington, DC, USA, July 10-16. 1:(6):1999;546-551.
27. Xu L. Temporal BYY learning for state space approach, hidden Markov model and blind source separation. IEEE Transactions on Signal Processing. 48:2000;2132-2144.
28. Xu L. BYY learning system and theory for parameter estimation, data smoothing based regularization and model selection. Neural, Parallel and Scientific Computations. 8:2000;55-82.
29. Xu L. BYY harmony learning, independent state space and generalized APT financial analyses. IEEE Transactions on Neural Networks. 12:(4):2001;822-849.
30. Xu L. Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, ME-RBF models and three-layer nets. International Journal of Neural Systems. 11:(1):2001;3-69.
31. Xu L. BYY harmony learning, structural RPCL, and topological self-organizing on mixture models. Neural Networks. 15:2002;1125-1151.
32. Xu L. BYY learning, regularized implementation, and model selection on modular networks with one hidden layer of binary units. Neurocomputing. 51:2003;277-301.
33. Xu L., Krzyzak A., Oja E. Rival penalized competitive learning for clustering analysis, RBF net and curve detection. IEEE Transactions on Neural Networks. 4:1993;636-649.
34. Xu L., Oja E. Randomized Hough transform (RHT): Basic mechanisms, algorithms and complexities. Computer Vision, Graphics, and Image Processing: Image Understanding. 57:(2):1993;131-154.