Functional Cluster Analysis via Orthonormalized Gaussian Basis Expansions and Its Application

Journal of Classification

Volumn 27, Issue 2, 2010, Pages 211-230

  Kayano, Mitsunori ^a   Dozono, Koji ^b   Konishi, Sadanori ^b  

^a KYOTO UNIVERSITY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

Cholesky decomposition; Functional data; Gram Schmidt orthonormalization; k means; Protein structure; Radial basis functions; Self Organizing Maps

Indexed keywords

EID: 77957020005     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-010-9054-8     Document Type: Article

References (22)

1. ABRAHAM, C., CORNILLON, P. A., MATZNER-LOBER, E., and MOLINARI, N. (2003), "Unsupervised Curve Clustering Using b-Splines", Scandinavian Journal of Statistics, 30(3), 581-595.
2. ANDO, T., KONISHI, S., and IMOTO, S. (2008), "Nonlinear Regression Modeling via Regularized Radial Basis Function Networks", Journal of Statistical Planning and Inference, 138(11), 3616-3633.
3. BISHOP, C. M. (1995), Neural Networks for Pattern Recognition, Oxford: Oxford University Press.
4. CIARLET, P. G. (1989), Introduction to Numerical Linear Algebra and Optimisation, Cambridge: Cambridge University Press.
5. DE BOOR, C. (2001), A Practical Guide to Splines (Rev. ed.), Berlin and Heidelberg: Springer.
6. DING, C. H., and DUBCHAK, I. (2001), "Multi-class Protein Fold Recognition Using Support Vector Machines and Neural Networks", Bioinformatics, 17, 349-358.
7. DUDA, R. O., HART, P. E., and STORK, D. G. (2001), Pattern Classification (2nd ed.), New York: Wiley-Interscience.
8. EILERS, P., and MARX, B. (1996), "Flexible Smoothing with B-Splines and Penalties (With Discussion)", Statistical Science, 11, 89-121.
9. GREEN, P. J., and MARDIA, K. V. (2006), "Bayesian Alignment Using Hierarchical Models, with Applications in Protein Bioinformatics", Biometrika, 93(2), 235-254.
10. GREEN, P. J., and SILVERMAN, B. W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, London: Chapman and Hall.
11. HARTIGAN, J. A., and WONG, M. A. (1978), "Algorithm as 136: A k-Means Clustering Algorithm", Applied Statistics, 28, 100-108.
12. IMOTO, S., and KONISHI, S. (2003), "Selection of Smoothing Parameters in B-Spline Nonparametric Regression Models Using Information Criteria", Annals of the Institute of Statistical Mathematics, 55(4), 671-687.
13. KAWANO, S., and KONISHI, S. (2007), "Nonlinear Regression Modeling via Radial Basis Functions", Bulletin of Informatics and Cybernetics, 39, 83-96.
14. KONISHI, S., and KITAGAWA, G. (1996), "Generalised Information Criteria in Model Selection", Biometrika, 83, 875-890.
15. KONISHI, S., and KITAGAWA, G. (2008), Information Criteria and Statistical Modeling, New York: Springer.
16. KOHONEN, T. (1997),] Self-Organizing Maps, Berlin: Springer.
17. MOODY, J., and DARKEN, C. J. (1989), "Fast Learning in Networks of Locally-tuned Processing Units", Neural Computation, 1, 281-294.
18. NGUYEN, M. N., and RAJAPAKSE, J. C. (2003), "Multi-class Support Vector Machines for Protein Secondary Structure Prediction", Genome Informatics, 14, 218-227.
19. RAMSAY, J. O., and LI, X. (1998), "Curve Registration", Journal of the Royal Statistical Society, Series B, 60(2), 351-363.
20. ROSSI, F., CONAN-GUEZ, B., and GOLLI, A. E. (2004), "Clustering Functional Data with the SOM Algorithm", Proceedings of European Symposium on Artificial Neural Networks Bruges, Belgium, Brussels: D-Facto Pub, pp. 305-312.
21. STRANG, G., and BORRE, K. (1997), Linear Algebra, Geodesy, and GPS, Wellesley MA: Wellesley-Cambridge Press.
22. WU, T. D., HASTIE, T., and SCHMIDLER, S. C. (1998), "Regression Analysis of Multiple Protein Structures", Journal of Computational Biology, 5(3), 585-596.