Robust extraction of local structures by the minimum β-divergence method

Neural Networks

Volumn 23, Issue 2, 2010, Pages 226-238

  Nurul Haque Mollah, Md ^a,b   Sultana, Nayeema ^c   Minami, Mihoko ^e   Eguchi, Shinto ^a,d  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^b UNIVERSITY OF RAJSHAHI   (Bangladesh)

^c Department of Statistics   (Bangladesh)

^d GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

^e KEIO UNIVERSITY   (Japan)

Author keywords

divergence; Adaptive selection for the tuning parameter; Cross validation; Initialization of the parameters; Local PCA; Sequential estimation

Indexed keywords

ADAPTIVE SELECTION; CROSS VALIDATION; DATA CLUSTERS; FINITE MIXTURE MODELS; INITIAL VALUES; LOCAL PRINCIPAL COMPONENT ANALYSIS; LOCAL STRUCTURE; OBSERVED DATA; PCA MODEL; ROBUST LEARNING ALGORITHM; SELECTION PROCEDURES; SEQUENTIAL ESTIMATION; STRUCTURE-BASED; TUNING PARAMETER;

LEARNING ALGORITHMS; SEQUENTIAL CIRCUITS; TUNING;

PRINCIPAL COMPONENT ANALYSIS;

ARTICLE; CONTROLLED STUDY; EXTRACTION; LEARNING ALGORITHM; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; SIMULATION; STATISTICAL MODEL;

ALGORITHMS; CLUSTER ANALYSIS; COMPUTER SIMULATION; DATABASES, FACTUAL; LEARNING; NORMAL DISTRIBUTION; PRINCIPAL COMPONENT ANALYSIS; TIME FACTORS;

EID: 73949119816     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2009.11.011     Document Type: Article

References (30)

1. Amari S.-I. Neural theory of association and concept formation. Biological Cybernetics 26 (1977) 175-185
2. Basu A., Harris I.R., Hjort N.L., and Jones M.C. Robust and efficient estimation by minimising a density power divergence. Biometrika 85 (1998) 549-559
3. Campbell N.A. Robust procedures in multivariate analysis 1: Robust co-variance estimation. Applied Statistics 29 (1980) 231-237
4. Croux C., and Haesbroeck G. Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies. Biometrika 87 (2000) 603-618
5. Figueiredo M., and Jain A.K. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 3 (2002) 381-396
6. Ghahramani Z., and Beal M.J. Variational inference for Bayesian mixture of factor analysers. Advances in neural information processing system Vol. 12 (2000) 449-455
7. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., and Stahel W.A. Robust statistics: The approach based on influence functions (1986), Wiley, New York
8. Haykin S. Neural networks (1999), Prentice Hall, Toronto
9. Hastie T., Tibshirani R., and Friedman J. The elements of statistical learning (2001), Springer, New York
10. Hotelling H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 24 (1933) 417-441
11. Higuchi I., and Eguchi S. The influence function of principal component analysis by self-organizing rule. Neural Computation 10 (1998) 1435-1444 82(397), 249-266
12. Higuchi I., and Eguchi S. Robust principal component analysis with adaptive selection for tuning parameters. Journal of Machine Learning Research 5 (2004) 453-471
13. Hinton G.E., Dayan P., and Revow M. Modeling the manifolds of images of handwritten digits. IEEE Transactions on Neural Networks 8 (1997) 65-74
14. Jolliffe I.T. Principal component analysis (2002), Springer
15. Kamiya H., and Eguchi S. A class of robust principal component vectors. Journal of Multivariate Analysis 76 (2001) 239-269
16. Kambhatla N., and Leen T.K. Dimension reduction by local principal component analysis. Neural Computation 9 (1997) 1493-1516
17. Kurihara K., Welling M., and Vlassis N. Accelerated variational dirichlet mixture models (2006), NIPS
18. Lee T.-W., Lewicki M.S., and Sejnowski T.J. ICA Mixture models for unsupervised classification of non-Gaussian classes and automatic context switching in blind signal separation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22 (2000) 1078-1089
19. Meinicke P., and Ritter H. Resolution-based complexity control for Gaussian mixture models (2001), Wiley, New York
20. Minami M., and Eguchi S. Robust blind source separation by beta-divergence. Neural Computation 14 (2002) 1859-1886
21. Minami, M., & Eguchi, S. (2003). Adaptive selection for minimum β-divergence method. In Proceedings of ICA-2003 conference
22. Mollah M.N.H., Minami M., and Eguchi S. Exploring latent structure of mixture ICA models by the minimum β-divergence method. Neural Computation 17 (2006) 166-190
23. Mollah M.N.H., Minami M., and Eguchi S. Robust prewhitening for ICA by minimizing beta-divergence and its application to FastICA. Neural Processing Letters 25 2 (2007) 91-110
24. Möller R., and Hoffmann H. An extension of neural gas to local PCA. Neurocomputing 62 (2004) 305-326
25. Oja E. Neural networks, principal components and subspace. Journal of Neural Systems 1 (1989) 61-68
26. Ridder, D., & France, V. (2003). Robust subspace mixture models using t-distributions. In Proc. british machine vision conference 2003 (pp. 319-328)
27. Su, T., & Dy, J.G. (2004). Automated hierarchical mixtures of probabilistic principal component analysers. In Proc. of 21st international conference on machine learning
28. Tipping M.E., and Bishop C.M. Mixtures of probabilistic principal component analysers. Neural Computation 11 2 (1999) 443-482
29. Xu L., and Yuille A. Robust principal component analysis by self-organizing rules based on statistical physics approach. IEEE Transactions on Neural Networks 6 (1995) 131-143
30. Zhang B., Fu M., and Yan H. A nonlinear neural network model of mixture of local principal component analysis: Application to handwritten digits recognition. Pattern Recognition 34 (2001) 203-214