Spatial Functional Principal Component Analysis with Applications to Brain Image Data

SFB 649 Discussion Paper 2017-024

31 Pages Posted: 11 Dec 2017

See all articles by Yingxing Li

Yingxing Li

Xiamen University

Chen Huang

Aarhus University - Department of Economics and Business Economics

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Date Written: December 11, 2017

Abstract

This paper considers a fast and effective algorithm for conducting functional principle component analysis with multivariate factors. Compared with the univariate case, our approach could be more powerful in revealing spatial connections or extracting important features in images. To facilitate fast computation, we connect Singular Value Decomposition with penalized smoothing and avoid estimating a huge dimensional covariance operator. Under regularity assumptions, the results indicate that we may enjoy the optimal convergence rate by employing the smoothness assumption inherent to functional objects. We apply our method on the analysis of brain image data. Our extracted factors provide excellent recovery of the risk related regions of interests in human brain and the estimated loadings are very informative in revealing the individual risk attitude.

Keywords: Principal Component Analysis; Penalized Smoothing; Asymptotics; Functional Magnetic Resonance Imaging (fMRI)

JEL Classification: C00

Suggested Citation

Li, Yingxing and Huang, Chen and Härdle, Wolfgang K., Spatial Functional Principal Component Analysis with Applications to Brain Image Data (December 11, 2017). SFB 649 Discussion Paper 2017-024 , Available at SSRN: https://ssrn.com/abstract=3085853 or http://dx.doi.org/10.2139/ssrn.3085853

Yingxing Li

Xiamen University ( email )

Xiamen, Fujian 361005
China

Chen Huang

Aarhus University - Department of Economics and Business Economics ( email )

Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Wolfgang K. Härdle (Contact Author)

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

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