Correlation-Based Functional Clustering via Subspace Projection
Journal
Journal of the American Statistical Association
Journal Volume
103
Journal Issue
484
Start Page
1684-1692
ISSN
0162-1459
1537-274X
Date Issued
2008-12-01
Author(s)
Pai-Ling Li
Abstract
A correlation-based functional clustering method is proposed for grouping curves with similar shapes. A correlation between two random functions defined through the functional inner product is used as a similarity measure. Curves with similar shapes are embedded in the cluster subspace spanned by a mean shape function and eigenfunctions of the covariance kernel. The cluster membership prediction for each curve attempts to maximize the functional correlation between the observed and predicted curves via shape standardization and subspace projection among all possible clusters. The proposed method accounts for shape differentials through the functional multiplicative random-effects shape function model for each cluster, which regards random scales and intercept shifts as a nuisance. A consistent estimate is proposed for the random scale effect, whose sample variance estimate is also consistent. The derived identifiability conditions for the clustering procedure unravel the predictability of cluster memberships. Simulation studies and a real data example illustrate the proposed method. © 2008 American Statistical Association.
Subjects
Functional correlation
Functional data
Functional principal component analysis
Projection
Random scale effects
Shape similarity.
Publisher
Informa UK Limited
Type
journal article