NDLI: Multi-dimensional functional principal component analysis

Content Provider	Springer Nature Link
Author	Chen, Lu Hung Jiang, Ci Ren
Copyright Year	2016
Abstract	Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general d-dimensional domain. The computational issues emerging in the extension are fully addressed with our proposed solutions. The local linear smoothing technique is employed to perform estimation because of its capabilities of performing large-scale smoothing and of handling data with different sampling schemes (possibly on irregular domain) in addition to its nice theoretical properties. Besides taking the fast Fourier transform strategy in smoothing, the modern GPGPU (general-purpose computing on graphics processing units) architecture is applied to perform parallel computation to save computation time. To resolve the out-of-memory issue due to large-scale data, the random projection procedure is applied in the eigendecomposition step. We show that the proposed estimators can achieve the classical nonparametric rates for longitudinal data and the optimal convergence rates for functional data if the number of observations per sample is of the order $$(n/ \log n)^{d/4}$$ . Finally, the performance of our approach is demonstrated with simulation studies and the fine particulate matter (PM 2.5) data measured in Taiwan.
Starting Page	1181
Ending Page	1192
Page Count	12
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	27
Issue Number	5
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2016-06-29
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fast Fourier transform Functional and longitudinal data GPU-parallelization Local linear smoother PM 2.5 data Random projection Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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