Skip to main content

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Anderson, T. W. (1984). An introduction to multivariate statistical analysis. New York: Wiley.

    MATH  Google Scholar 

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

    Article  MathSciNet  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Ferraty, F., & Vieu, P. (2006). Nonparametric functional data analysis: Theory and practice. New York: Springer.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Krzyśko, M., & Wołyński, W. (2009). New variants of pairwise classification. European Journal of Operational Research, 199(2), 512–519.

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  Google 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.

    Book  MATH  Google 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.

    Article  MathSciNet  MATH  Google 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.

    Article  Google Scholar 

  • Rossi, F., Delannayc, N., Conan-Gueza, B., & Verleysenc, M. (2005). Representation of functional data in neural networks. Neurocomputing, 64, 183–210.

    Article  Google 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.

    Article  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tomasz Górecki .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Górecki, T., Krzyśko, M., Wołyński, W. (2016). Multivariate Functional Regression Analysis with Application to Classification Problems. In: Wilhelm, A., Kestler, H. (eds) Analysis of Large and Complex Data. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-25226-1_15

Download citation

Publish with us

Policies and ethics