We propose a new approach, the forward functional testing (FFT) procedure, to cluster number selection for functional data clustering. We present a framework of subspace projected functional data clustering based on the functional multiplicative random-effects model, and propose to perform functional hypothesis tests on equivalence of cluster structures to identify the number of clusters. The aim is to find the maximum number of distinctive clusters while retaining significant differences between cluster structures. The null hypotheses comprise equalities between the cluster mean functions and between the sets of cluster eigenfunctions of the covariance kernels. Bootstrap resampling methods are developed to construct reference distributions of the derived test statistics. We compare several other cluster number selection criteria, extended from methods of multivariate data, with the proposed FFT procedure. The performance of the proposed approaches is examined by simulation studies, with applications to clustering gene expression profiles. 本文提出一個FFT(forward functional testing)程序來決定依組函數型資料的最適分群數。我們根據函數型相呈隨機效應模式發展出函數型資料的子空間投影分群方法，並利用函數型假設檢定判斷不同群組之間結構的異同，而檢定結果將作為FFT方法確認資料最適分群數的依據，FFT方法的主要目的是過有系統的拔靴法檢定過程，得到能讓所有相異分群之結構均達到顯著差一時的吹大分群數，而群組結構間的比較特徵則著重於資料的平均函數與特徵空間，此外，本文亦將幾個多變量群數選取準則延伸應用至函數型資料上，並與所提出的FFT方法做比較。本文最後透過數值模擬研究與兩組實際基因表現量資料之分析來驗證FFT方法的可行性與相對表現。
關聯:
Computational Statistics & Data Analysis 55(6), pp.2090-2103
