基於迭代式分群之時空函數型資料多重變點偵測方法

Abstract

時空函數型資料中的多變點偵測是一項具有挑戰性的問題，尤其當不同空間位置具有不同變點結構時更加困難。現有方法通常假設所有位置具有相同的變點結構，或是對各位置分別偵測變點；前者可能忽略空間異質性，後者則較難利用不同位置之間的相似性。本研究提出一個新的框架，先估計各位置的局部變點，再根據空間距離與變點集合相似性對空間位置進行分群，並透過迭代程序更新分群結果與群內共同變點估計。此方法可處理多個變點，並在共享群內資訊的同時保留空間異質性。模擬結果顯示，在具有分群式變點結構的情境下，所提出的方法能改善群內共同變點估計，且相較於全域共同變點方法能更有效地描述異質的變點結構。

Change-point detection in spatio-temporal functional data is challenging, especially when different spatial locations have different change-point structures. Existing methods usually assume a common change-point structure across all locations or detect change-points separately at each location. The former may overlook spatial heterogeneity, while the latter may not fully use the similarity among locations. We propose a new framework that first estimates local change-points, clusters spatial locations based on spatial distance and change-point set similarity, and updates the clustering results and cluster-wise common change-point estimates iteratively. The method can handle multiple change-points while sharing information within clusters and preserving spatial heterogeneity. Simulation results show that, in clustered change-point settings, the proposed method improves cluster-wise common change-point estimation and better captures heterogeneous change-point structures than a global common change-point method.