Multiscale Adaptive Functional Principal Components Analysis and Its Application in the Neuroimaging Data

• Activity Number: 405
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Japing Wang*+ and Hongtu Zhu
• Companies: ENAR/IMS/ASA and The University of North Carolina
• Keywords: multiscale adpative ; functional PCA ; neuroimaging data ; Adaptive neighborhood ; smoothing ; kernel estimate

Abstract

In the functional principle component analysis (fPCA), the raw data often need to be smoothed. The common way is to smooth each observed functional data by either spline or local weighted smoothing method. For example, in neuroimaging data, one assumes voxels are independent then implement the fPCA. However, for the spatio-temporal data, the voxels are spatial dependent. Thus we propose a new approach to find the functional principle components, called multiscale adaptive fPCA. Compared with the existing fPCA, our method has three unique features: being spatial, being hierarchical, and being adaptive. Our approach analyzes all observations in the ellipsoid of each voxel and these consecutively connected ellipsoids across all voxels can capture spatial dependence among imaging observations. This method combines imaging observations with adaptive weights in the voxels within the ellipsoid of the current voxel to adaptively and spatially smooth functional images. Finally, this approach applies the smoothed functional data to the fPCA. Simulation studies and real data analysis are used to demonstrate the methodology and examine the performance of the adaptive estimates.