Wavelet-RKHS-based functional statistical classification

Advances in Data Analysis and Classification

Volumn 6, Issue 3, 2012, Pages 201-217

  Rincon M ^a   Ruiz Medina, M D ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Functional data analysis; Gene expression profiles; Penalized logistic regression; Reproducing kernel Hilbert space; Wavelet decomposition; Yeast cell cycle

Indexed keywords

COMPUTATION THEORY; GENE EXPRESSION; GRADIENT METHODS; HILBERT SPACES; LOGISTIC REGRESSION; VECTOR SPACES; YEAST;

FUNCTIONAL DATA ANALYSIS; GENE EXPRESSION PROFILES; PENALIZED LOGISTIC REGRESSION; REPRODUCING KERNEL HILBERT SPACES; YEAST CELL CYCLES;

WAVELET DECOMPOSITION;

EID: 84867063756     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-012-0112-4     Document Type: Article

References (29)

1. Abramovich F, Angelini C (2006) Testing in mixed-effects FANOVA models. J Stat Plan Inference 136: 4326-4348.
2. Angelini C, De Canditiis D, Leblanc F (2003) Wavelet regression estimation in nonparametric mixed effect models. J Multivar Anal 85: 267-291.
3. Araki Y, Konishi S, Kawano S, Matsui H (2009a) Functional regression modeling via regularized Gaussian basis expansions. Ann Inst Stat Math 61: 811-833.
4. Araki Y, Konishi S, Kawano S, Matsui H (2009b) Functional logistic discrimination via regularized basis expansions. Commun Stat Theory Methods 38: 2944-2957.
5. Cardot H, Sarda P (2005) Estimation in generalized linear model for functional data via penalized likelihood. J Multivar Anal 92: 24-41.
6. Ferraty F, Vieu P (2006) Nonparameric functional data analysis. Springer, New York.
7. Hall P, Poskitt D, Presnell B (2001) A functional data-analytic approach to signal discrimination. Technometrics 43: 1-9.
8. Kawano S, Konishi S (2009) Nonlinear logistic discrimination via regularized Gaussian basis expansions. Commun Stat Simul Comput 38: 1414-1425.
9. Konishi, Kitagawa G (1996) Generalised information criteria in model selection. Biometrika 83: 875-890.
10. Konishi S, Ando T, Imoto S (2004) Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika 91: 27-43.
11. Leng X, Müller HG (2006) Classification using functional data analysis for temporal gene expression data. Bioinformatics 22: 68-76.
12. Lian H (2007) Nonlinear functional models for functional responses in reproducing kernel Hilbert spaces. Canad J Stat 35: 597-606.
13. McCullagh P, Nelder JA (1989) Generalized linear models. Chapman & Hall, London.
14. Mendelson S (2002) Learnability in Hilbert spaces with reproducing kernels. J Complexity 18: 152-170.
15. Müller HG (2005) Functional modelling and classification of longitudinal data. Cand J Stat 32: 223-240.
16. Müller HG, Stadtmüller U (2005) Generalized functional linear models. Ann Stat 33: 774-805.
17. Picard R, Cook D (1984) Cross-validation of regression models. J Am Stat Assoc 79: 575-583.
18. Preda C (2007) Regression models for functional data by reproducing kernel Hilbert spaces methods. J Stat Plann Inference 137: 829-840.
19. Rachdi M, Vieu P (2007) Nonparametric regression for functional data: automatic smoothing parameter selection. J Stat Plann Inference 137: 2784-2801.
20. Ramsay J, Silverman BW (2005) Functional data analysis Springer series in statistics. Springer: New York.
21. Rincón M, Ruiz-Medina MD (2012) Local wavelet-vaguelette-based functional classification of gene expression data. Biometrical J 54: 75-93.
22. Ruiz-Medina MD, Salmerón R (2010) Functional maximum-likelihood estimation of ARH(p) models. Stoch Environ Res Risk Assess 24: 131-146.
23. Schölkopf B, Smola A (2002) Learning with kernels. MIT Press, Cambridge.
24. Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, Brown PO, Botstein D, Futcher B (1998) Comprehensive identification of cell-cycle regulated genes of the yeast Saccharomyces cerevisiae by microarray hibridization. Mol Biol Cell 9: 3273-3297.
25. Triebel H (1978) Interpolation theory, function spaces, differential operators. North-Holland, Amsterdam.
26. Vakhania NN, Tarieladze VI, Chebonyan SA (1987) Probability distributions in banach spaces. D. Reidel Publishing Company, Dordrecht.
27. Vidakovic B (2006) Statistical modelling by wavelets. Wiley, New York.
28. Yang JY, Peng ZL, Yu Z, Zhang R-J, Anh V, Wang D (2009) Prediction of protein structural classes by recurrence quantification analysis based on chaos game representation. J Theor Biol 257: 618-626.
29. Yang J-Y, Yu Z, Anh V (2009) Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids. Chaos Solitons Fractals 40: 607-620.