Correlation-Based Functional Clustering via Subspace Projection

• 成果类型: Article
• 署名作者: Chiou, Jeng-Min; Li, Pai-Ling
• 署名单位: Tamkang University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214508000000814
• 发表日期: 2008
• 页码: 1684-1692
• 关键词: gene-expression; effects model

摘要

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 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 identifiablility conditions for the clustering procedure unravel the predictability of cluster memberships. Simulation and a real data example illustrate the proposed method.