Abstract
The Partial Least Squares (PLS) approach is used for the clusterwise linear regression algorithm when the set of predictor variables forms an L 2-continuous stochastic process. The number of clusters is treated as unknown and the convergence of the clusterwise algorithm is discussed. The approach is compared with other methods via an application to stock-exchange data.
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References
Aguilera, A. M., Ocaña, F., and Valderrama, M. J. (1998). “An Approximated Principal Component Prediction Model for Continuous-Time Stochastic Process,” Applied Stochastic Models and Data Analysis, 11, 61–72.
Bock, H.-H. (1969). “The Equivalence of Two Extremal Problems and Its Application to the Iterative Classification of Multivariate Data,” in Lecture notes, Mathematisches Forschungsinstitut Oberwolfach.
Charles, C. (1977). Régression Typologique et Reconnaissance des Formes, Ph.D. disseration, Université Paris IX, Paris, France.
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. (1974). “Méthodes Statistiques et Numériques de l’Analyse Harmonique,” Annales de l’INSEE (France), 5, 3–101.
Deville, J. C. (1978). “Analyse et Prévision des Séries Chronologiques Multiples Non Stationnaires,” Statistique et Analyse des Données (France), 3, 19–29.
Hennig, C. (1999). “Models and Methods for Clusterwise Linear Regression,” Classification in the Information Age, Berlin: Springer, pp. 179–187.
Hennig, C. (2000). “Identifiability of Models for Clusterwise Linear Regression,” Journal of Classification, 17, 273–296.
Plaia, A. (2001). “On the Number of Clusters in Clusterwise Linear Regression,” in Proceedings of the Xth International Symposium on Applied Stochastic Models and Data Analysis, pp. 847–852.
Preda, C. (1999). “Analyse Factorielle d’un Processus: Problèmes d’Approximation et de Régression,” doctoral thesis, Université de Lille 1, Lille, France.
Preda, C, and Saporta, G. (2002). “Régression PLS sur un Processus Stochastique,” Revue de Statistique Appliquée, 50, 27–45.
Ramsay, J. O., and Silverman, B. W. (1997). Functional Data Analysis, Springer-Verlag, New York.
Saporta, G. (1981). “Méthodes Exploratoires d’Analyse de Données Temporelles,” Cahiers du B.U.R.O, Technical Report 37, Université Pierre et Marie Curie, Paris, France.
Spaeth, H. (1979). “Clusterwise Linear Regression,” Computing, 22, 367–373.
Tenenhaus, M. (1998). La Régression PLS: Théorie et Pratique. Editions Technip, Paris.
Wold, S., Ruhe, A. and Dunn III, W. J. (1984). “The Collinearity Problem in Linear Regression: The Partial Least Squares (PLS) Approach to Generalized Inverses,” SI AM Journal on Scientific and Statistical Computing, 5, 765–743.
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Preda, C., Saporta, G. (2004). PLS Approach for Clusterwise Linear Regression on Functional Data. In: Banks, D., McMorris, F.R., Arabie, P., Gaul, W. (eds) Classification, Clustering, and Data Mining Applications. Studies in Classification, Data Analysis, and Knowledge Organisation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17103-1_17
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DOI: https://doi.org/10.1007/978-3-642-17103-1_17
Publisher Name: Springer, Berlin, Heidelberg
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