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Wavelet-RKHS-based functional statistical classification

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  • M. Rincón
  • M. Ruiz-Medina

Abstract

A functional classification methodology, based on the Reproducing Kernel Hilbert Space (RKHS) theory, is proposed for discrimination of gene expression profiles. The parameter function involved in the definition of the functional logistic regression is univocally and consistently estimated, from the minimization of the penalized negative log-likelihood over a RKHS generated by a suitable wavelet basis. An iterative descendent method, the gradient method, is applied for solving the corresponding minimization problem, i.e., for computing the functional estimate. Temporal gene expression data involved in the yeast cell cycle are classified with the wavelet-RKHS-based discrimination methodology considered. A simulation study is developed for testing the performance of this statistical classification methodology in comparison with other statistical discrimination procedures. Copyright Springer-Verlag 2012

Suggested Citation

  • M. Rincón & M. Ruiz-Medina, 2012. "Wavelet-RKHS-based functional statistical classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 201-217, October.
    • Handle: RePEc:spr:advdac:v:6:y:2012:i:3:p:201-217
    DOI: 10.1007/s11634-012-0112-4
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    References listed on IDEAS

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    1. Yang, Jian-Yi & Yu, Zu-Guo & Anh, Vo, 2009. "Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 607-620.
    2. Angelini, Claudia & De Canditiis, Daniela & Leblanc, Frédérique, 2003. "Wavelet regression estimation in nonparametric mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 267-291, May.
    3. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    4. Yuko Araki & Sadanori Konishi & Shuichi Kawano & Hidetoshi Matsui, 2009. "Functional regression modeling via regularized Gaussian basis expansions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 811-833, December.
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