Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains

Journal of the American Statistical Association

Volumn 113, Issue 522, 2018, Pages 649-659

  Happ, Clara ^a   Greven, Sonja ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Dimension reduction; Functional data analysis; Image analysis; Multivariate functional data

Indexed keywords

EID: 85041532049     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2016.1273115     Document Type: Article

References (31)

1. Allen, G., (2013), Multi-way Functional Principal Components Analysis, in IEEE 5th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 220–223.
2. Berrendero, J., Justel, A., and Svarc, M., (2011), “Principal Components for Multivariate Functional Data,” Computational Statistics & Data Analysis, 55, 2619–2634.
3. Blennow, K., Leon, M., and Zetterberg, H., (2006), “Alzheimer’s Disease,” Lancet, 368, 387–403.
4. Bosq, D., (2000), Linear Processes in Function Spaces, New York: Springer.
5. Carroll, J. D., and Chang, J. J., (1970), “Analysis of Individual Differences in Multidimensional Scaling via An n-Way Generalization of ‘Eckart-Young’ Decomposition,” Psychometrika, 35, 283–319.
6. Cattell, R., (1966), “The Scree Test for the Number of Factors,” Multivariate Behavioral Research, 1, 245–276.
7. Chiou, J.-M., Yang, Y.-F., and Chen, Y.-T., (2014), Multivariate Functional Principal Component Analysis: A Normalization Approach,” Statistica Sinica, 24, 1571–1596.
8. Coppi, R., and Bolasco, S., (eds.) (1989), Multiway Data Analysis, Amsterdam: North-Holland.
9. Crainiceanu, C., Reiss, P., Goldsmith, J., Huang, L., Huo, L., and Scheipl, F., (2014), refund: Regression with Functional Data, R Package Version 0.1-14.
10. Eilers, P., and Marx, B., (1996), “Flexible Smoothing with B-splines and Penalties,” Statistical Science, 11, 89–121.
11. Hall, P., and Horowitz, J. L., (2007), “Methodology and Convergence Rates for Functional Linear Regression,” Annals of Statistics, 35, 70–91.
12. Hall, P., and Hosseini-Nasab, M., (2006), “On Properties of Functional Principal Components Analysis,” Journal of the Royal Statistical Society, Series B, 68, 109–126.
13. Happ, C., (2017a), funData: An S4 Class for Functional Data in R, R Package Version 1.0.
14. ——— (2017b), MFPCA: Multivariate Functional Principal Component Analysis, R Package Version 1.0-1.
15. ——— (2017c), “Object-Oriented Software for Functional Data,” arXiv 1707.02129.
16. Huang, J. Z., Shen, H., and Buja, A., (2009), “The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions,” Journal of the American Statistical Association, 104, 1609–1620.
17. Jacques, J., and Preda, C., (2014), “Model-Based Clustering for Multivariate Functional Data,” Computational Statistics & Data Analysis, 71, 92–106.
18. Lu, H., Plataniotis, K. N., and Venetsanopoulos, A., (2013), Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data, Boca Raton, FL: CRC Press.
19. Mercer, J., (1909), “Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations,” Philosophical Transactions A, 209, 415–446.
20. Mueller, S., Weiner, M., Thal, L., Petersen, R., Jack, C., Jagust, W., Trojanowski, J., Toga, A., and Beckett, L., (2005), “Ways Toward an Early Diagnosis in Alzheimer’s Disease: The Alzheimer’s Disease Neuroimaging Initiative (ADNI),” Alzheimer’s & Dementia, 1, 55–66.
21. Müller, H. G., and Stadtmüller, U., (2005), “Generalized Functional Linear Models,” Annals of Statistics, 33, 774–805.
22. Ramsay, J., and Silverman, B., (2005), Functional Data Analysis (2nd ed.), New York: Springer.
23. Ramsay, J., Wickham, H., Graves, S., and Hooker, G., (2014), fda: Functional Data Analysis, R Package Version 2.4.4.
24. Reed, M., and Simon, B., (1980), Methods of Modern Mathematical Physics. I: Functional Analysis (rev. and enl. ed.), San Diego, CA: Academic Press.
25. Ruigrok, A., Salimi-Khorshidi, G., Lai, M.-C., Baron-Cohen, S., Lombardo, M., Tait, R., and Suckling, J., (2014), “A Meta-Analysis of Sex Differences in Human Brain Structure,” Neuroscience and Biobehavioral Reviews, 39, 34–50.
26. Saporta, G., (1981), “Méthodes Exploratoires d’analyse de Données Temporelles,” Ph.D. dissertation, Université Pierre et Marie Curie, Paris.
27. Tucker, L. R., (1966), “Some Mathematical Notes on Three-Mode Factor Analysis,” Psychometrika, 31, 279–311.
28. Werner, D., (2011), Funktionalanalysis (7th ed.), Berlin: Springer.
29. Yao, F., Müller, H.-G., and Wang, J.-L., (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590.
30. Yu, Y., Wang, T., and Samworth, R. J., (2015), “A Useful Variant of the Davis-Kahan Theorem for Statisticians,” Biometrika, 102, 315–323.
31. Zemyan, S., (2012), The Classical Theory of Integral Equations, Basel: Birkhäuser.