Classification problems  based on regression models for multi-dimensional functional data

Tomasz Górecki; Mirosław Krzysko; Waldemar Wołynski

doi:https://doi.org/10.59170/stattrans-2015-006

Classification problems based on regression models for multi-dimensional functional data

Tomasz Górecki Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poland , Mirosław Krzysko Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poland , Waldemar Wołynski Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poland. Statistics in Transition new series, vol. 16, 2015, 1, pages: 97-110 Published online: 2 March 2015 https://doi.org/10.59170/stattrans-2015-006

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ABSTRACT

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. We use multivariate functional regression techniques for the classification of multivariate functional data. The approaches discussed are illustrated with an application to two real data sets.

KEYWORDS

multivariate functional data, functional data analysis, multivariate functional regression, classification.

REFERENCES

ANDERSON, T. W., (1984). An Introduction to Multivariate Statistical Analysis. Wiley, New York.

ANDO, T., (2009). Penalized optimal scoring for the classification of multi dimensional functional data. Statistcal Methodology 6, 565–576.

BESSE, P., (1979). Etude descriptive d’un processus. Ph.D. thesis, Université Paul Sabatier.

EFRON, B., HASTIE, T., JOHNSTONE, I., TIBSHIRANI, R., (2004). Least Angle Regression. Annals of Statistics 32(2), 407–499.

FERRATY, F., VIEU, P., (2003). Curve discrimination. A nonparametric functional approach. Computational Statistics & Data Analysis 44, 161–173.

FERRATY, F., VIEU, P., (2006). Nonparametric Functional Data Analysis: Theory and Practice. Springer, New York.

FERRATY, F., VIEU, P., (2009). Additive prediction and boosting for functional data. Computational Statistics & Data Analysis 53(4), 1400–1413.

GÓRECKI, T., KRZYŚKO, M., (2012). Functional Principal Components Analysis. In: J. Pociecha and R. Decker (Eds.): Data analysis methods and its applications. C. H. Beck, Warszawa, 71–87.

GÓRECKI, T, KRZYŚKO, M., WASZAK, Ł., WOŁYŃSKI, W., (2014).Methods of reducing dimension for functional data. Statistics in Transition new series 15, 231–242.

HASTIE, T. J., TIBSHIRANI, R. J., BUJA, A., (1995). Penalized discriminant analysis. Annals of Statistics 23, 73–102.

JAMES, G. M., (2002). Generalized linear models with functional predictors. Journal of the Royal Statistical Society 64(3), 411–432.

JACQUES, J., PREDA, C., (2014). Model-based clustering for multivariate functional data. Computational Statistics & Data Analysis 71, 92–106.

KRZYŚKO, M., WOŁYŃSKI, W., (2009). New variants of pairwise classification. European Journal of Operational Research 199(2), 512–519.

MATSUI, H., ARAKI, Y., KONISHI, S., (2008). Multivariate regression modeling for functional data. Journal of Data Science 6, 313–331.

MÜLLER, H. G., STADMÜLLER, U., (2005). Generalized functional linear models. Annals of Statistics 33, 774–805.

NADARAYA, E. A., (1964). On Estimating Regression. Theory of Probability and its Applications 9(1), 141–142.

OLSZEWSKI, R. T., (2001). Generalized Feature Extraction for Structural Pattern Recognition in Time-Series Data. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA.

RAMSAY, J. O., SILVERMAN, B. W., (2005). Functional Data Analysis. Springer, New York.

REISS, P. T., OGDEN R. T., (2007). Functional principal component regression and functional partial least squares. Journal of the American Statistcal Assosiation 102(479), 984–996.

ROSSI, F., DELANNAYC, N., CONAN-GUEZA, B., VERLEYSENC, M.,(2005). Representation of functional data in neural networks. Neurocomputing 64, 183–210.

ROSSI, F., VILLA, N., (2006). Support vector machines for functional data classification. Neural Computing 69, 730–742.

ROSSI, N., WANG, X., RAMSAY, J. O., (2002). Nonparametric item response function estimates with EM algorithm. Journal of Educational and Behavioral Statistics 27, 291–317.

RODRIGUEZ, J. J., ALONSO, C. J., MAESTRO, J. A., (2005). Support vector machines of intervalbased features for time series classification. Knowledge Based Systems 18, 171–178.

SAPORTA, G., (1981). Méthodes exploratoires d’analyse de données temporelles, these de doctorat d’état es sciences mathématiques soutenue le 10 juin 1981, Université Pierre et Marie Curie.

SHMUELI, G., (2010). To explain or to predict? Statistical Science 25(3), 289–310.

TIBSHIRANI, R., (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58(1), 267–288.

WATSON, G. S., (1964). Smooth regression analysis. Sankhya – The Indian Journal of Statistics, Series A 26(4), 359–372.

WOLD, H., (1985). Partial least squares. In: S. Kotz, and N.L. Johnson (Eds.): Encyclopedia of statistical sciences vol. 6, Wiley, New York, 581–591.