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Jia-Tong Jiang

2011-04-08
12:45:00 - 14:45:00

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Organizing functional data into sensible groupings is one of the most fundamental modes of understanding and learning the underlying mechanism generating functional data. Clustering analysis is often employed to search for homogeneous subgroups of individuals in a data set. In Abraham et al. (2003, Scandinavian Journal of Statistics), they start with feature extraction on the mean function and use k-means clustering procedure to determine the clusters. In Peng and Muller (2008, Annals of Applied Statistics), feature extraction on the mean function is infeasible due to the sparsity of available observations for each curve. Instead, they assume common mean function for all units and start with feature extraction on the covariance function. However, the clusters found by k-means clustering procedure can be explained through the characteristics of mean function of each unit. This motivates a theoretical study on comparing the utilities of these two approaches under the settings of densely observed functional data. In this talk, we will only present the case that the size of clusters is two only. We will present analysis on the lose of efficiency with feature extraction on the covariance function.