Analysis of Large and Complex Data pp 173-183 | Cite as
Multivariate Functional Regression Analysis with Application to Classification Problems
Conference paper
First Online:
Abstract
Multivariate functional data analysis is an effective approach to dealing with multivariate and complex data. These data are treated as realizations of multivariate random processes; the objects are represented by functions. In this paper we discuss different types of regression model: linear and logistic. Various methods of representing functional data are also examined. The approaches discussed are illustrated with an application to two real data sets.
Keywords
Linear Discriminant Analysis Functional Data Classification Classification Multivariate Sample Functional Data Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
- Anderson, T. W. (1984). An introduction to multivariate statistical analysis. New York: Wiley.MATHGoogle Scholar
- Ando, T. (2009). Penalized optimal scoring for the classification of multi-dimensional functional data. Statistcal Methodology, 6, 565–576.MathSciNetCrossRefGoogle Scholar
- Besse, P. (1979). Etude descriptive d’un processus. Ph.D. thesis, Universit’e Paul Sabatier.Google Scholar
- Ferraty, F., & Vieu, P. (2003). Curve discrimination. A nonparametric functional approach. Computational Statistics & Data Analysis, 44, 161–173.MathSciNetCrossRefMATHGoogle Scholar
- Ferraty, F., & Vieu, P. (2006). Nonparametric functional data analysis: Theory and practice. New York: Springer.MATHGoogle Scholar
- Ferraty, F., & Vieu, P. (2009). Additive prediction and boosting for functional data. Computational Statistics & Data Analysis, 53(4), 1400–1413.MathSciNetCrossRefMATHGoogle Scholar
- Górecki, T., & Krzyśko, M. (2012). Functional Principal components analysis. In J. Pociecha & R. Decker (Eds.), Data analysis methods and its applications (pp. 71–87). Warszawa: C.H. Beck.Google Scholar
- Hastie, T. J., Tibshirani, R. J., & Buja, A. (1995). Penalized discriminant analysis. Annals of Statistics, 23, 73–102.MathSciNetCrossRefMATHGoogle Scholar
- Jacques, J., & Preda, C. (2014). Model-based clustering for multivariate functional data. Computational Statistics & Data Analysis, 71, 92–106.MathSciNetCrossRefGoogle Scholar
- James, G. M. (2002). Generalized linear models with functional predictors. Journal of the Royal Statistical Society, 64(3), 411–432.MathSciNetCrossRefMATHGoogle Scholar
- Krzyśko, M., & Wołyński, W. (2009). New variants of pairwise classification. European Journal of Operational Research, 199(2), 512–519.MathSciNetCrossRefMATHGoogle Scholar
- Li, Y., Wang, N., & Carroll, R. J. (2010). Generalized functional linear models with semi para-metric single-index interactions. Journal of the American Statistical Association, 105(490), 621–633.MathSciNetCrossRefMATHGoogle Scholar
- Matsui, H., Araki, Y., & Konishi, S. (2008). Multivariate regression modeling for functional data. Journal of Data Science, 6, 313–331.Google Scholar
- Müller, H. G., Stadmüller, U. (2005). Generalized functional linear models. Annals of Statistics, 33, 774–805.MathSciNetCrossRefGoogle Scholar
- Olszewski, R. T. (2001). Generalized Feature Extraction for Structural Pattern Recognition in Time-Series Data. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
- Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis. New York: Springer.CrossRefMATHGoogle Scholar
- 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.MathSciNetCrossRefMATHGoogle Scholar
- Rodriguez, J. J., Alonso, C. J., & Maestro, J. A. (2005). Support vector machines of interval based features for time series classification. Knowledge-Based Systems, 18, 171–178.CrossRefGoogle Scholar
- Rossi, F., Delannayc, N., Conan-Gueza, B., & Verleysenc, M. (2005). Representation of functional data in neural networks. Neurocomputing, 64, 183–210.CrossRefGoogle Scholar
- Rossi, F., & Villa, N. (2006). Support vector machines for functional data classification. Neural Computing, 69, 730–742.Google Scholar
- 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.CrossRefGoogle Scholar
- Saporta, G. (1981). Methodes exploratoires d’analyse de donn’ees temporelles. Ph.D. thesis, Cahiers du Buro.Google Scholar
- Shmueli, G. (2010). To explain or to predict? Statistical Science, 25(3), 289–310.MathSciNetCrossRefMATHGoogle Scholar
Copyright information
© Springer International Publishing Switzerland 2016