Abstract
Clusterwise regression is applied to functional data, using PCR and PLS as regularization methods for the functional linear regression model. We compare these two approaches on simulated data as well as on stock-exchange data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ABRAHAM, C., CORNILLON, P., MATZNER-LÖBER, E. and MOLINARI, N. (2003): Unsupervised curve clustering using B-splines. Scand. J. Statist., 30, 581–595.
BARKER, M. and RAYENS, W. (2003): Partial least squares for discrimination. Journal of Chemometrics, 17, 166–173.
BOCK, H.-H. (1989): The equivalence of two extremal problems and its application to the iterative classification of multivariate data. Lecture note, Mathematisches Forschungsinstitut Oberwolfach.
CHARLES, C. (1977): Régression Typologique et Reconnaissance des Formes. Thèse de doctorat, Université Paris IX.
DE JONG, S. (1993): PLS fits closer than PCR. Journal of Chemometrics, 7, 551–557.
DESARBO, W.S. and CRON, W.L. (1988): A maximum likelihood methodology for clusterwise linear regression. Journal of Classification, 5, 249–282.
DEVILLE, J.C. (1978): Analyse et prévision des séries chronologiques multiples non stationnaires. Statistique et Analyse des Données, 3, 19–29.
DIDAY, E. (1976): Classification et sélection de paramètres sous contraintes. Rapport de Recherche IRIA-LABORIA, no. 188.
ESCABIAS, M., AGUILERA, A.M., and VALDERRAMA, M.J. (2004): Principal component estimation of functional logistic regression: discussion of two different approaches. Journal of Nonparametric Statistics, 3–4, 365–385.
ESCOUFIER, Y. (1970) Echantillonage dans une population de variables aléatoires réelles. Publications de l’Institut de Statistique de l’Université de Paris, 19, Fasc. 4, 1–47.
FERRATY, F. and VIEU, P. (2006): Nonparametric Functional Data Analysis. Theory and Practice. Springer Series in Statistics.
HENNIG, C. (1999): Models and methods for clusterwise linear regression. In: Classification in the Information Age, Springer, Berlin, 179–187.
HENNIG, C. (2000): Identifiability of models for Clusterwise linear regression. Journal of Classification, 17, 273–296.
PLAIA, A. (2004): Constrained clusterwise linear regression. In: M. Vichi, P. Monari, S. Mignani, A. Montanari (Eds): New Developments in Classification and Data Analysis, Springer, 78–86.
PHATAK, A. and DE HOOG, F. (2001): PLSR, Lanczos, and conjugate gradients. CSIRO Mathematical & Information Sciences, Report No. CMIS 01/122, Canberra.
PREDA, C. and SAPORTA, G. (2005a): PLS regression on a stochastic process. Computational Statistics and Data Analysis, 48, 149–158.
PREDA, C. and SAPORTA, G. (2005b): Clusterwise PLS regression on a stochastic process. Computational Statistics and Data Analysis, 49, 99–108.
PREDA, C., SAPORTA, G. and LÉVÉDER, C. (2007): PLS classification of functional data. Computational Statistics, In Press, doi: 10.1007/s00180-007-0041-4.
RAMSAY, J.O. and SILVERMAN, B.W. (1997): Functional Data Analysis. Springer Series in Statistics, Springer-Verlag, New York.
RAMSAY, J.O. and SILVERMAN, B.W. (2002): Applied Functional Data Analysis. Methods and Case Studies. Springer, Berlin-Heidelberg.
SAPORTA, G. (1981): Méthodes exploratoires d’analyse de données temporelles. Cahiers du B.U.R.O., No. 37-38, Université Pierre et Marie Curie, Paris.
SPAETH, H. (1979): Clusterwise linear regression. Computing 22, 367–373.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Preda, C., Saporta, G. (2007). PCR and PLS for Clusterwise Regression on Functional Data. In: Brito, P., Cucumel, G., Bertrand, P., de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73560-1_56
Download citation
DOI: https://doi.org/10.1007/978-3-540-73560-1_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73558-8
Online ISBN: 978-3-540-73560-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)