Clustering the Sptatio-Temporal Functional Data with Multiscale Adaptive Smoothing Method and EM-Based Algorithm

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jiaping Wang*+ and Hongtu Zhu
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: Adaptive weights ; Multiscale adaptive ; Voxel-wise approach ; Discrete wavelet transform ; EM algorithm ; Clustering

Abstract

The study of the spatio-temporal functional data like the fMRI data often aims to analyze functional data with complex spatial and temporal correlation structures and varying activation patterns on a two-dimensional (2D) surface or in a 3D volume. One way to obtain this spatial pattern is to use the clustering method. The goal of this paper is to propose an algorithm, called multiscale adaptive smoothing and clustering(MASC), consisted of two steps to smooth and cluster the spatio-temporal functional data, which will automatically find the number of the clusters. Since the spatio-temporal functional data are spatial and temporal dependent, a smoothing approach is necessary before clustering. A multiscale adaptive procedure is proposed to smooth the data, which combines spatial observations with adaptive weights in the locations within the ellipsoid of the current location to adaptively and spatially smooth functional data. Then an EM-based clustering method is proposed in the wavelet domain by transforming the smoothed curves into the wavelet coefficients.Two simulation studies and a real data analysis are used to demonstrate the methodology and examine its finite sample performace