10.25673/122860">


Proceedings of International Conference on Applied Innovation in IT
2025/12/22, Volume 13, Issue 5, pp.265-272

Dimensionality Reduction of Multivariate Functional Data Using FPCA


Alaa H. Jalob and Lekaa Ali Mohamed


Abstract: In many scientific and engineering applications, data are collected over discrete, often equidistant, time intervals. While such data can be analyzed using traditional statistical methods, these methods are often very limited in their ability to capture the underlying continuous nature of dynamic processes of the phenomenon under study. This study aims to present and develop a statistical methodology for analysing multivariate functional data characterised by structural complexity, nonlinear properties, and continuous nature of its observations and variables. By using the Functional Principal Component Analysis (FPCA) method to analyse high-dimensional data through dimensionality reduction, and accurately discovering structural patterns in the data without relying on fixed distributional assumptions. Also, improving model selection using the Bayesian Information Criterion (BIC), which determines the optimal number of orthogonal basis functions and enhances the model's fit to the complexity of the data, thereby contributing to the accuracy of the analysis and understanding of relationships within the functional data.

Keywords: Functional Data Analysis, Multivariate Functional Data, Orthonormal Basis Expansion, Functional Principal Component Analysis, Covariance Function, Dimensionality Reduction.

DOI: 10.25673/122860

Download: PDF

References:

  1. J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2nd ed. Springer, 2005.
  2. T. Hsing and R. Eubank, Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. Wiley, 2015.
  3. J. Jacques and C. Preda, “Functional data analysis: A review,” Computational Statistics & Data Analysis, vol. 71, pp. 1–15, 2014.
  4. I. T. Jolliffe, Principal Component Analysis, 2nd ed. Springer, 2002.
  5. L. Xiao, V. Zipunnikov, D. Ruppert, and C. Crainiceanu, “Fast covariance estimation for high-dimensional functional data,” Statistics and Computing, vol. 26, no. 1, pp. 409–421, 2016.
  6. K. Chen and J. Lei, “Localizing the functional principal components analysis of irregularly sampled longitudinal data,” Stat, vol. 6, no. 1, pp. 147–161, 2017.
  7. J. Wei, L. Zhou, and L. Zhang, “Model selection using modified AIC and BIC in joint modeling of paired functional data,” Statistics & Probability Letters, vol. 80, no. 23–24, pp. 1918–1924, 2010.
  8. H. Helena, R. Pardo, M. Vega, E. Barrado, J. M. Fernandez, and L. Fernandez, “Temporal evolution of groundwater composition in an alluvial aquifer (Pisuerga River, Spain) by principal component analysis,” Water Research, vol. 34, no. 3, pp. 807–816, 2000.
  9. T. Górecki, M. Krzyśko, Ł. Waszak, and W. Wołyński, “Selected statistical methods of data analysis for multivariate functional data,” Statistical Papers, vol. 59, no. 1, pp. 153–182, 2018.
  10. X. Dai and H.-G. Müller, “Principal component analysis for functional data on Riemannian manifolds and spheres,” The Annals of Statistics, vol. 46, no. 6A, pp. 3334–3361, 2018.
  11. Y. Lu, X. Zhou, E. Cui, D. Rogers, C. M. Crainiceanu, J. Wrobel, and A. Leroux, “Generalized conditional functional principal component analysis,” arXiv preprint arXiv:2411.10312, Nov. 2024.
  12. G. Aneiros, R. Cao, R. Fraiman, C. Genest, and P. Vieu, “Recent advances in functional data analysis and high-dimensional statistics,” Journal of Multivariate Analysis, vol. 170, pp. 3–9, 2019.
  13. K. Kim and P. Piotr, “Extremal dependence measure for functional data,” Journal of Multivariate Analysis, vol. 184, p. 104746, 2022.

    HOME

       - Conference
       - Journal
       - Paper Submission to Conference
       - Paper Submission to Journal
       - Fee Payment
       - For Authors
       - For Reviewers
       - Important Dates
       - Conference Committee
       - Editorial Board
       - Reviewers
       - Last Proceeding


    PROCEEDINGS

       - Volume 13, Issue 5 (ICAIIT 2025)
       - Volume 13, Issue 4 (ICAIIT 2025)
       - Volume 13, Issue 3 (ICAIIT 2025)
       - Volume 13, Issue 2 (ICAIIT 2025)
       - Volume 13, Issue 1 (ICAIIT 2025)
       - Volume 12, Issue 2 (ICAIIT 2024)
       - Volume 12, Issue 1 (ICAIIT 2024)
       - Volume 11, Issue 2 (ICAIIT 2023)
       - Volume 11, Issue 1 (ICAIIT 2023)
       - Volume 10, Issue 1 (ICAIIT 2022)
       - Volume 9, Issue 1 (ICAIIT 2021)
       - Volume 8, Issue 1 (ICAIIT 2020)
       - Volume 7, Issue 1 (ICAIIT 2019)
       - Volume 7, Issue 2 (ICAIIT 2019)
       - Volume 6, Issue 1 (ICAIIT 2018)
       - Volume 5, Issue 1 (ICAIIT 2017)
       - Volume 4, Issue 1 (ICAIIT 2016)
       - Volume 3, Issue 1 (ICAIIT 2015)
       - Volume 2, Issue 1 (ICAIIT 2014)
       - Volume 1, Issue 1 (ICAIIT 2013)


    LAST CONFERENCE

       ICAIIT 2026
         - Photos
         - Reports

    PAST CONFERENCES

    ETHICS IN PUBLICATIONS

    ACCOMODATION

    CONTACT US

 

        

         Proceedings of the International Conference on Applied Innovations in IT by Anhalt University of Applied Sciences is licensed under CC BY-SA 4.0


                                                   This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License


           ISSN 2199-8876
           Publisher: Edition Hochschule Anhalt
           Location: Anhalt University of Applied Sciences
           Email: leiterin.hsb@hs-anhalt.de
           Phone: +49 (0) 3496 67 5611
           Address: Building 01 - Red Building, Top floor, Room 425, Bernburger Str. 55, D-06366 Köthen, Germany

        site traffic counter

Creative Commons License
Except where otherwise noted, all works and proceedings on this site is licensed under Creative Commons Attribution-ShareAlike 4.0 International License.