Fundamentals, challenges, and advances of statistical learning for knowledge discovery and problem solving: A BYY harmony perspective

Proceedings of 2005 International Conference on Neural Networks and Brain Proceedings, ICNNB'05

Volumn 1, Issue , 2005, Pages

  Xu, Lei ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

DATA HANDLING; INTELLIGENT AGENTS; KNOWLEDGE ACQUISITION; NUMERICAL METHODS; PROBLEM SOLVING; STATISTICAL METHODS;

KNOWLEDGE DISCOVERY; LEARNING THEORIES; MATHEMATICAL REPRESENTATIONS; TEMPORAL EXTENSIONS;

LEARNING SYSTEMS;

EID: 33847155556     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (146)

1. Akaike, H (1974), "A new look at the statistical model identification", IEEE Tr. Automatic Control, 19, 714-723.
2. Akaike, H (1981), "Likelihood of a model and information criteria", Journal of Econometrics, 16, 3-14.
3. Akaike, H (1987), "Factor analysis and AIC", Psychometrika, 52, 317-332.
4. Amari, S., Chen, TP., & Cichocki, A. (1997), "Stability analysis of adaptive blind source separation", Neural Networks, 10, 1345-1351.
5. Amari, SI, Cichocki, A, & Yang, HH (1996), "A new learning algorithm for blind separation of sources", in DS Touretzky, et al, eds, Advances in Neural Information Processing 8, MIT Press, 757-763.
6. Anderson, TW, & Rubin, H (1956), "Statistical inference in factor analysis", Proc. Berkeley Symp. Math. Statist. Prob. 3rd 5, UC Berkeley, 111-150.
7. Attias, H. (1999), "Independent factor analysis", Neural Computation, 11, 803-851.
8. Baldi, P, & Brunak, S (2001), Bioinformatics: The Machine Learning Approach, The MIT Press, Cambridge, MA.
9. Baldi, P. & Hornik, K.(1991). "Back-propagation and unsupervised learning in linear networks,", in Y. Chauvin and D. E. Rumelhart (Eds.), Back Propagation: Theory, Architectures and Applications. Erlbaum Associates, 1991.
10. Bartholomew, DJ & Knott, M., (1999). "Latent variable models and factor analysis", Kendall's Library of Satisfies, Vol. 7, Oxford University Press, New York, 1999.
11. Belkin, M. and Niyogi, P., (2003), "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Computation,15(6), pp1373-1396.
12. Bell, A & Sejnowski, T (1995), "An information maximization approach to blind separation and blind deconvolution", Neural Computation, 17, 1129-1159.
13. Belouchrani, A., & Cardoso, JF, (1995), "Maximum likelihood source separation by the expectation-maximization technique: deterministic and stochastic implementation", Proc. NOLTA95, 49-53.
14. Bishop, C., Svensen, M. and Williams, C. (1998) "GTM: The generative topographic mapping", Neural Computation, 10, pp215-234.
15. Bollerslev,T.(1986), "Generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 31, 307-327.
16. Bourlard, H & Kamp, Y (1988), "Auto-association by multilayer Perceptrons and singular value decomposition", Biol. Cyb. 59, 291-294.
17. Bozdogan, H (1987) "Model Selection and Akaike's Information Criterion: The general theory and its analytical extension", Psychometrika, 52, 345-370.
18. Bozdogan, H & Ramirez, DE (1988), "FACAIC: Model selection algorithm for the orthogonal factor model using AIC and FACAIC", Psychometrika, 53 (3), 407-415.
19. Brockett, RW (1991), "Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems", Linear Algebra and Its Applications, 146, 79-91.
20. Carpenter, GA & Grossberg, S., (1987), "A massively parallel architecture for a self-organizing neural pattern recognition machine", Computer Vision, Graphics, and Image Processing, Vol.37, 54-115.
21. Cavanaugh, JE (1997), "Unifying the derivations for the Akaike and corrected Akaike information criteria", Statistics & Probability Letters, 33, 201-208.
22. Chan, KY, Chu, WS, & Xu, L (2003), "Experimental Comparison between two computational strategies for topological self-organization", Proc. of IDEAL03, Lecture Notes in Computer Science, LNCS 2690, Springer-Verlag, pp410-414.
23. Chen, TP, & Amari, S. (2001), "Unified Stabilization Approach to principal and minor components extraction algorithm," Neural Networks, 14, 1377-1387.
24. Cheung, CC & Xu, L. (2000), "Some Global and Local Convergence Analysis on The Information-Theoretic Independent Component Analysis Approach", Neurocomputing, 30, 79-102.
25. Cooper, G & Herskovitz, E (1992), "A Bayesian method for the induction of probabilistic networks from data", Machine Learning, 9, 309-347.
26. Comon, P (1994), "Independent component analysis - a new concept?", Signal Processing 36, 287-314.
27. Cox,T. and Cox, M. (1994), Multidimensional Scaling, Chapman&Hall, London.
28. Dayan, P. & Hinton, GE (1995), "The Helmholtz machine", Neural Computation 7, No.5, 889-904.
29. Dempster, AP, Laird, NM, & Rubin, DB, (1977), "Maximum -likelihood from incomplete data via the EM algorithm", J. of Royal Statistical Society, B39, 1-38.
30. Devijver, PA, & Kittler, J (1982), Pattern Recognition: A Statistical Approach, Prentice-Hall.
31. Devroye, L, et al (1996), A Probability Theory of Pattern Recognition, Springer.
32. DiCiccio, TJ, et al, (1997), "Computing Bayes factors by combining simulations and asymptotic Approximations", Journal of the American Statistical Association, 92 (439), 903-915.
33. Duda, RO, & Hart, PE (1973), Pattern classification and Scene analysis, Wiley.
34. Efron, B & Tibshirani, R (1993), An Introduction to the Bootstrap, Chaoman and Hall, New York .
35. Everson, R., & Roberts, S. (1999), "Independent component analysis: A fexible nonlinearity and decorrelating manifold approach", Neural Computation, 11, pp1957-1983.
36. Gaeta, M, & Lacounme, JL (1990), "Source Separation without a priori knowledge: the maximum likelihood solution", in Proc. EVSIPCO90, 621-624.
37. Girolami, M. (1998), "An alternative perspective on adaptive independent component analysis algorithms", Neural Computation, 10, 2103-2114.
38. Girosi, F, et al, (1995) "Regularization theory and neural architectures", Neural Computation, 7, 219-269.
39. Han, J, & Kamber, M (2001), Data Mining: Concepts and Techniques, Morgan Kaufmann, 2001.
40. Hinton, GE, Dayan, P, Frey, BJ, & Neal, RN (1995), "The wakesleep algorithm for unsupervised learning neural networks", Science 268, 1158-1160.
41. Hinton, GE & Zemel, RS (1994), "Autoencoders, minimum description length and Helmholtz free energy", Advances in NIPS, 6, 3-10.
42. Hotelling, H (1936), "Simplified calculation of principal components", Psychometrika 1, 27-35.
43. Hough, PVC, (1962) "Method and means for recognizing complex patterns, U.S. Patent 3069654, Dec.18, 1962.
44. Hu, XL & Xu, L (2005), "An Improved BYY Data Smoothing Learning Criterion for Selecting Subspace Dimension", in preparation.
45. Hu, XL & Xu, L (2004), "A Comparative Investigation on Subspace Dimension Determination", Neural Networks, Vol. 17, (2004), 1051-1059.
46. Hu, XL & Xu, L (2004), "Investigation on Several Model Selection Criteria for Determining the Number of Cluster", Neural Information Processing - Letters and Reviews, Vol.4, No.1, July 2004, pp. 1-10.
47. Hurvich, CM, & Tsai, CL (1989), "Regression and time series model in samll samples", Biometrika, 76, 297-307.
48. Hyvarinen, A., Karhunen, J., & Oja, A. (2001), Independent Component Analysis, John Wileys & Sons, Inc., New York.
49. Illingworth, J. & Kittler, J., (1988), "A survey of the Hough Transform", Comput. Vision Graphics and Image Process. 43, 221-238.
50. Jutten, C & Herault, J (1988), "Independent Component Analysis versus Principal Component Analysis", Proc. EUSIPCO88, 643-646.
51. Kalman, RE, "A New Approach to linear filtering and prediction problems", Trans. ASME-J Basic Engineering, March, 35-45, 1960.
52. Kälviäinen, H., Hirvonen, P., Xu, L., & Oja, E. (1995), "Probabilistic and Non-probabilistic Hough Transforms: Overview and Comparisons", Image and Vision Computing, Vol.5, No. 4, pp.239-252.
53. Karhunen, J.(1982), "On the recursive estimation of the eigenvectors of correlation type matrics", Lic. Tech. Thesis, Helsinki University of Technology.
54. Karhunen, J. & Joutsensalo, J. (1994), "Representation and separation of signals using nonlinear PCA type learning", Neural Networks, 7(1), 113-127.
55. Kashyap, RL (1982), "Optimal choice of AR and MA parts in autoregressive and moving-average models", IEEE Trans. PAMI, 4, 99-104.
56. Kawamoto, M. (2002), "Cerebellum and Motor Cobtrol", The Handbook of Brain Theory and Neural Networks, Second edition, (MA Arbib, Ed.), Cambridge, MA: The MIT Press, pp190-195.
57. Kohonen, T (1982), "Self-organized formation of topologically correct feature maps", Biological Cybernetics 43, 59-69.
58. Kohonen, T (1995), Self-Organizing Maps, Springer-Verlag, Berlin.
59. Lee, T., Girolami, M., & Sejnowski, T. (1999). "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources". Neural Computation, 11, 409-433.
60. Liu, ZY, Chiu, KC, and Xu, L (2004), "The One-bit-Matching Conjecture for Independent Component Analysis", Neural Computation, Vol. 16, No. 2, pp. 383-399.
61. Liu, ZY, Chiu, KC, and Xu, L (2003), "Strip Line Detection and Thinning by RPCL-Based Local PCA", Pattern Recognition Letters 24, pp2335-2344, 2003.
62. Liu, ZY, Chiu, KC, and Xu, L (2003), "Improved system for object detection and star/galaxy classification via local subspace analysis", Neural Networks 16, (2003) 437-451.
63. Lu, W., & Rajapakse, J. (2000), "A neural network for under complete Independent Component Analysis", In Proc. 8th European Symposium on Artificial Neural Networks, Bruges, Belgium.
64. Ma, J, Wang, T, & Xu, L (2004), "A gradient BYY harmony learning rule on Gaussian mixture with automated model selection", Neurocomputing 56, 481-487.
65. Mackey, D (1992a) "A practical Bayesian framework for backpropagation", Neural Computation, 4, 448-472.
66. Mackey, D (1992b) "Bayesian Interpolation", Neural Computation, 4, 405-447.
67. von der Malsburg, Ch (1973), "Self-organization of orientation sensitive cells in the striate cortex", Kybernetik 14, 85-100.
68. Moulines, E., Cardoso, J., & Gassiat, E. (1997), "Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models", Proc. ICASSP97, 3617-3620.
69. McDonald, R (1985), Factor Analysis and Related Techniques, Lawrence Erlbaum.
70. McLachlan, GJ & Krishnan, T (1997) The EM Algorithm and Extensions, John Wiley & Son, INC.
71. Neath, AA & Cavanaugh, JE (1997), "Regression and Time Series model selection using variants of the Schwarz information criterion", Communications in Statistics A, 26, 559-580.
72. Oja, E. (1982), "A simplified neuron model as a principal component analyzer", Journal of Mathematical Biology, 16, 267-273.
73. Oja, E. (1989). Neural networks, principal components, and subspaces", International Journal of Neural Systems, 1, 61-68.
74. Pearlmutter, B., & Parra, L. (1996). "A context-sensitive generalization of ICA", Proc. ICONIP96, 151-157.
75. Pham, DT, Garrat, P., & Jutten, C. (1992), "Separation of a mixture of independent sources through a maximum likelihood approach", Proc. EUSIPCO92, 771-774.
76. Rabiner, L & Juang, BH (1993), Fundamentals of Speech Recognition, Prentice Hall, Inc.
77. Redner, RA & Walker, HP (1984), "Mixture densities, maximum likelihood, and the EM algorithm", SIAM Review, 26, 195-239.
78. Ridder, DD, Duin, D., & Kittler, R (2002), "Texture description by independent components", in Proc. the Joint International workshop on syntactical and structural pattern recognition, Windsor, Canada.
79. Rissanen, J (1986), "Stochastic complexity and modeling", Annals of Statistics, 14(3), 1080-1100.
80. Rissanen, J (1989), Stochastic Complexity in Statistical Inquiry, World Scientific: Singapore.
81. Rivals, I & Personnaz, L (1999) "On Cross Validation for Model Selection", Neural Computation, 11, 863-870.
82. Roweis, S. and Saul, LK, (2000), "Nonlinear Dimensionality Reduction by Locally Linear Embedding", Science, 290, 22 December 2000, pp2323-2326.
83. Rubi, D & Thayer, D (1976), "EM algorithm for ML factor analysis", Psychometrika 57, 69-76.
84. Rumelhart, DE, Hinton, GE, & Williams, RJ (1986), "Learning internal representations by error propagation", Parallel Distributed Processing, 1, MIT press.
85. Schwarz, G (1978), "Estimating the dimension of a model", Annals of Statistics, 6, 461-464.
86. Stone, M (1977), "An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion", J. Royal Statistical Society B, 39 (1), 44-47.
87. Stone, M (1978), "Cross-validation: A review", Math. Operat. Statist., 9, 127-140.
88. Stone, M (1979), "Comments on model selection criteria of Akaike and Schwartz. J. Royal Statistical Society B, 41 (2), 276-278.
89. Sugiura, N (1978), "Further analysis of data by Akaike's infprmation criterion and the finite corrections", Communications in Statistics A, 7, 12-26.
90. Tenenbaum, JB, Silva, J, and Langford, JC, (2000), "A Global Geometric Framework for Nonlinear Dimensionality Reduction", Science, 290, 22 December 2000, pp2319-2323.
91. Tikhonov, AN & Arsenin, VY (1977), Solutions of Ill-posed Problems, Winston and Sons.
92. Tong, L, Inouye, Y, & Liu, R (1993) "Waveform-preserving blind estimation of multiple independent sources", IEEE Trans. on Signal Processing 41, 2461-2470.
93. Wallace, CS & Boulton, DM (1968), "An information measure for classification", Computer Journal, 11, 185-194.
94. Wallace, CS & Freeman, PR (1987), "Estimation and inference by compact coding", J. of the Royal Statistical Society, 49(3), 240-265.
95. Wallace, CS & Dowe, DR (1999), "Minimum message length and Kolmogorov complexity", Computer Journal, 42 (4), 270-280.
96. Welling, M., & Weber, M. (2001), "A constrained EM algorithm for independent component analysis", Neural Computation, 13, 677-689.
97. Vapnik, VN (1995), The Nature Of Statistical Learning Theory, Springer-Verlag.
98. Xu, L. (2005), "A5 Problem Solving Paradigm: A Unified Perspective and New Results on RHT Computing, Mixture Based Learning, and Evidence Combination", invited and featured talk, Proc. of IEEE International Conference on Granular Computing, Beijing, 25-27 July 2005, pp70-77.
99. Xu, L. (2005),"One-Bit-Matching ICA Theorem, Convex-Concave Programming, and Combinatorial Optimization", Lecture Notes in Computer Science, Vol 3496: Advances in Neural Networks. A plenary talk on Second International Symposium on Neural Networks, May 30 - June 1, 2005, Springer-Verlag, pp5-20.
100. Xu, L. (2004), "Temporal BYY Encoding, Markovian State Spaces, and Space Dimension Determination", IEEE Trans on Neural Networks, Vol. 15, No. 5, pp1276-1295.
101. Xu, L (2004), "Advances on BYY harmony learning: information theoretic perspective, generalized projection geometry, and independent factor auto-determination", IEEE Trans on Neural Networks, Vol. 15, No. 4, pp885-902.
102. Xu, L. (2004), "Bayesian Ying Yang Learning (I): A Unified Perspective for Statistical Modeling", Intelligent Technologies for Information Analysis, N. Zhong and J. Liu (eds), Springer, pp615-659.
103. Xu, L. (2004), "Bayesian Ying Yang Learning (II): A New Mechanism for Model Selection and Regularization", Intelligent Technologies for Information Analysis, N. Zhong and J. Liu (eds), Springer, pp661-706.
104. Xu, L. (2004), "Bi-directional BYY Learning for Mining Structures with Projected Polyhedra and Topological Map", Invited talk, in Proc. of FDM 2004: Foundations of Data Mining, eds., T.Y.Lin, S.Smale, T. Poggio, and C.J. Liau, Brighton, UK, Nov. 01, 2004, pp5-18.
105. Xu, L. (2003), "BYY Learning, Regularized Implementation, and Model Selection on Modular Networks with One Hidden Layer of Binary Units", Neurocomputing, Vol.51, p227-301.
106. Xu, L. (2003), "Data smoothing regularisation, multi-sets-learning, and problem solving strategies", Neural Networks, Vol. 15, Nos. 5-6, 817-825.
107. Xu, L. (2003), "Independent Component Analysis and Extensions with Noise and Time: A Bayesian Ying-Yang Learning Perspective", Neural Information Processing Letters and Reviews, Vol.1, No.1, 1-52.
108. Xu, L (2002), "BYY Harmony Learning, Structural RPCL, and Topological Self-Organizing on Mixture Models ", Neural Networks, Vol. 15, Nos. 8-9, 1125-1151.
109. Xu, L, (2002), "Bayesian Ying Yang Harmony Learning", The Handbook of Brain Theory and Neural Networks, Second edition, (MA Arbib, Ed.), Cambridge, MA: The MIT Press, pp1231-1237.
110. Xu, L (2001), "BYY Harmony Learning, Independent State Space and Generalized APT Financial Analyses ", IEEE Trans on Neural Networks, 12 (4), 822-849.
111. Xu, L (2001), "Best Harmony, Unified RPCL and Automated Model Selection for Unsupervised and Supervised Learning on Gaussian Mixtures, Three-Layer Nets and ME-RBF-SVM Models", Intl J of Neural Systems 11 (1), 43-69.
112. Xu, L (2001), "An Overview on Unsupervised Learning from Data Mining Perspective", Advances in Self-Organizing Maps, Nigel Allison, et al eds, Springer-Verlag, June, pp181-210 (2001).
113. Xu, L (2000), "Temporal BYY Learning for State Space Approach, Hidden Markov Model and Blind Source Separation", IEEE Trans on Signal Processing 48, 2132-2144.
114. Xu, L (1998), "Bayesian Kullback Ying-Yang Dependence Reduction Theory", Neurocomputing 22 (1-3), 81-112, 1998.
115. Xu, L (1998), "RBF Nets, Mixture Experts, and Bayesian Ying-Yang Learning", Neurocomputing, Vol. 19, No. 1-3, 223-257.
116. Xu, L(1998), "Bayesian Ying-Yang Learning Theory For Data Dimension Reduction and Determination", Journal of Computational Intelligence in Finance, Finance & Technology Publishing, Vol.6, No.5, pp 6-18, 1998.
117. Xu, L, (1998), Rival Penalized Competitive Learning, Finite Mixture, and Multisets Clustering, Proc. of IJCNN98, May 5-9, 1998, Anchorage, Alaska, Vol.II, pp2525-2530.
118. Xu, L, Cheung, CC, & Amari, SI (1998) "Learned Parametric Mixture Based ICA Algorithm", Neurocomputing 22 (1-3), 69-80.
119. Xu, L, Cheung, CC, & Amari, SI (1998), "Further Results on Nonlinearity and Separation Capability of A Linear Mixture ICA Method and Learned Parametric Mixture Algorithm", Proc. I&ANN'98, Feb. 9-10, 1998, Tenerife, Spain, pp39-44.
120. Xu, L (1997),"Bayesian Ying-Yang System and Theory as A Unified Statistical Learning Approach: (I) Unsupervised and Semi-Unsupervised Learning", in S Amari and N Kassabov eds, Brain-like Computing and Intelligent Information Systems, Springer-Verlag, pp241-274.
121. Xu, L (1997), "Bayesian Ying-Yang System and Theory as A Unified Statistical Learning Approach (II): From Unsupervised Learning to Supervised Learning and Temporal Modeling", in KM. Wong, et al, eds, Theoretical Aspects of Neural Computation: A Multidisciplinary Perspective, Springer-Verlag, pp25-42.
122. Xu, L (1997), "Bayesian Ying-Yang System and Theory as A Unified Statistical Learning Approach (III): Models and Algorithms for Dependence Reduction, Data Dimension Reduction, ICA and Supervised Learning", in KM. Wong, et al, eds, Theoretical Aspects of Neural Computation: A Multidisciplinary Perspective, Springer-Verlag, pp43-60.
123. Xu, L (1997), "Bayesian Ying-Yang Machine, Clustering and Number of Clusters", Pattern Recognition Letters 18, No.11-13, 1167-1178.
124. Xu, L, Cheung, CC, Yang, HH, & Amari, SI (1997), "Independent Component Analysis by The Information-Theoretic Approach with Mixture of Density", Proc. IJCNN97, Vol. III, 1821-1826.
125. Xu, L, Cheung, CC, Ruan, J, & Amari, SI (1997), "Nonlinearity and Separation Capability: Further Justification for the ICA Algorithm with A Learned Mixture of Parametric Densities", Proc. ESANN97, Bruges, April 16-18, 1997, pp291-296.
126. Xu, L (1997), "Bayesian Ying-Yang Learning Based ICA Models", Proc. 1997 IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing VII, Sept. 24-26, 1997, Florida, pp476-485.
127. Xu, L. Yang, HH, & Amari, SI (1996), "Signal Source Separation by Mixtures Accumulative Distribution Functions or Mixture of Bell-Shape Density Distribution Functions", Research Proposal, presented at FRONTIER FORUM (speakers: D. Sherrington, S. Tanaka, L.Xu & J. F. Cardoso), organized by S.Amari, S.Tanaka & A.Cichocki, RIKEN, Japan, April 10, 1996.
128. Xu, L, (1996), "A Unified Learning Scheme: Bayesian-Kullback YING-YANG Machine", Advances in Neural Information Processing Systems, 8, 444-450.
129. Xu, L, & Jordan, MI (1996), "On convergence properties of the EM algorithm for Gaussian mixtures", Neural Computation, 8, No.1, 1996, 129-151.
130. Xu, L, (1995), "Bayesian-Kullback Coupled YING-YANG Machines: Unified Learnings and New Results on Vector Quantization", Proc. Intl. Conf. on Neural Information Processing (ICONIP96), Oct 30-Nov.3, 1995, Beijing, China, pp977-988.
131. Xu, L (1995), "A unified learning framework: multisets modeling learning," Proceedings of 1995 World Congress on Neural Networks, vol.1, pp35-42.
132. Xu, L, (1995), "Advances on Three Streams of PCA Studies", Invited Talk, Proc. of 1995 IEEE Intl. Conf. on Neural Networks and Signal Processing, Dec. 10-13, 1995, Nanjing, Vol.I, pp480-483.
133. Xu, L, Jordan, MI, & Hinton, GE (1995), "An Alternative Model for Mixtures of Experts", Advances in Neural Information Processing Systems 7, eds, Cowan, JD, et al, MIT Press, 633-640, 1995.
134. Xu, L, & Yuille, AL (1995), "Robust Principal Component Analysis by Self-Organizing Rules Based on Statistical Physics Approach", IEEE Trans. on Neural Networks, Vol.6, No.1, 131-143.
135. Xu, L, (1994), "Multisets Modeling Learning: An Unified Theory for Supervised and Unsupervised Learning", Invited Talk, Proc. IEEE ICNN94, June 26-July 2, 1994, Orlando, Florida, Vol.1, pp.315-320.
136. Xu, L, Krzyzak, A, & Yuille, AL (1994), "On Radial Basis Function Nets and Kernel Regression: Statistical Consistency, Convergence Rates and Receptive Field Size", Neural Networks, 7, 609-628.
137. Xu, L, Krzyzak, A & Oja, E (1993), "Rival Penalized Competitive Learning for Clustering Analysis, RBF net and Curve Detection", IEEE Tr. on Neural Networks 4, 636-649.
138. Xu, L & Oja, E. (1993), "Randomized Hough Transform (RHT): Basic Mechanisms, Algorithms and Complexities", Computer Vision, Graphics, and Image Processing : Image Understanding, Vol.57, No.2, pp. 131-154.
139. Xu, L (1991&93) "Least mean square error reconstruction for self-organizing neural-nets", Neural Networks 6, 627-648, 1993. Its early version on Proc. IJCNN91'Singapore, 2363-2373, 1991.
140. Xu, L, Krzyzak, A & Oja, E (1992), "Unsupervised and Supervised Classifications by Rival Penalized Competitive Learning", Proc. of 11th Intl Conf. on Pattern Recognition (ICPR92), Aug.30-Sept.3, 1992, Hauge, Netherlands, Vol.1, pp.672-675.
141. Xu, L., & Jordan, M. (1992), "Thoeretical and experimental studies of the EM algorithm fo Unsupervised learning based on finite Gaussin mixture", MIT Computational Cognitive Science, Tech. Rep. 9302, Dept. of Brain and Cognitive Science, MIT Cambridge, MA.
142. Xu, L., Oja, E., & Suen, C.Y. (1992), "Modified Hebbian learning for curve and surface fitting", Neural Networks, 5, pp393-407.
143. Xu, L., Krzyzak, A., & Suen, C.Y. (1992), "Several Methods for Combining Multiple Classifiers and Their Applications in Handwritten Character Recognition", IEEE Trans. on System, Man and Cybernetics, Vol. SMC-22, No.3, pp.418-435.
144. Xu, L., Krzyzak, A., & Oja, E. (1991), "A Neural Net for Dual Subspace Pattern Recognition Methods", Intl J. of Neural Systems, 2(3), 169-184.
145. Xu, L, Oja, E., & Kultanen, P. (1990), "A New Curve Detection Method: Randomized Hough Transform (RHT)", Pattern Recognition Letters, Vol.11, pp.331-338.
146. Zhang, B. L., Xu, L., & Fu, M. Y. (1996), "Learning Multiple Causes by Competition Enhanced Least Mean Square Error Reconstruction", Intl J. of Neural Systems, 7(3), 223-236.