In this paper, the scale response functional multivariate regression model is considered. By using the basis functions representation of functional predictors and regression coefficients, this model is rewritten as a multivariate regression model. This representation of the functional multivariate regression model is used for multiclass classification for multivariate functional data. Computational experiments performed on real labelled data sets demonstrate the effectiveness of the proposed method for classification for functional data
functional data analysis, multi-label classification problem, multivariate functional data, regression
BACHE, K., LICHMAN, M., (2013). UCI Machine Learning Repository. Irvine,CA: University of California, School of Information and Computer Science (http://archive.ics.uci.edu/ml).
BERRENDERO, J. R., JUSTEL, A., SVARC, M., (2011). Principal Components for Multivariate Functional Data. Computational Statistics & Data Analysis,55, 2619–2634.
COLLAZOS, J. A. A., DIAS, R., ZAMBOM, A. Z., (2016). Consistent Variable Selection for Functional Regression Models. Journal of Multivariate Analysis,146, 63–71.
FERRATY, F., VIEU, P., (2006). Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer.
GÓRECKI, T., KRZYSKO, M., WASZAK, Ł., WOŁY ´ NSKI, W., (2016). Selected ´Statistical Methods of Data Analysis for Multivariate Functional Data. Statis tical Papers (Accepted) doi:10.1007/s00362-016-0757-8.
GÓRECKI, T., KRZYSKO, M., WOŁY ´ NSKI, W., (2015). Classification Problem ´Based on Regression Models for Multidimensional Functional Data. Statistics in Transition new series, 16, 97–110.
GÓRECKI, T., SMAGA, Ł., (2017). Multivariate Analysis of Variance for Func tional Data. Journal of Applied Statistics, 44, 2172–2189.
HORVÁTH, L., KOKOSZKA, P., (2012). Inference for Functional Data with Ap plications, New York: Springer.
JACQUES, J., PREDA, C., (2014). Model-Based Clustering for Multivariate Func tional Data. Computational Statistics & Data Analysis, 71, 92–106.
KAYANO, M., KONISHI, S., (2009). Functional Principal Component Analysis via Regularized Gaussian Basis Expansions and its Application to Unbalanced Data. Journal of Statistical Planning and Inference, 139, 2388–2398.
KRZYSKO, M., WASZAK, Ł., (2013). Canonical Correlation Analysis for Func- ´tional Data. Biometrical Letters, 50, 95–105.
KRZYSKO, M., WOŁY ´ NSKI, W., GÓRECKI, T., SKORZYBUT, M., (2008). ´Learning Systems, Warsaw: WNT (in Polish).
MATSUI, H., (2014). Variable and Boundary Selection for Functional Data via Multiclass Logistic Regression Modeling. Computational Statistics & Data Analysis, 78, 176–185.
MATSUI, H., KONISHI, S., (2011). Variable Selection for Functional Regression Models via the L1 Regularization. Computational Statistics & Data Analysis,55, 3304–3310.
OLSZEWSKI, R. T., (2001). Generalized Feature Extraction for Structural Pattern Recognition in Time-Series Data. Ph.D. Thesis, Carnegie Mellon University,Pittsburgh, PA (http://www.cs.cmu.edu/bobski).
RAMSAY, J. O., SILVERMAN, B. W., (2005). Functional Data Analysis, Second Edition, New York: Springer.
R DEVELOPMENT CORE TEAM, (2015). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Aus tria (https://www.R-project.org/).
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.
SHMUELI, G., (2010). To Explain or to Predict? Statistical Science, 25, 289–310.
ZHANG, J.-T., (2013). Analysis of Variance for Functional Data, London: Chap man & Hall