交通大學、清華大學 統計學研究所 專題演講
題 目：Correlation-Based Functional Clustering via Subspace Projection
主講人：李百靈教授 (淡江大學統計系)
時 間：98年11月20日(星期五)上午10:40-11:30
(上午10:20-10:40茶會於交大統計所429室舉行)
地 點：交大綜合一館427室
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 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.
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