基於累計離群分數之函數型資料線上變點偵測

Abstract

函數型資料出現在工程監測、生醫訊號、環境科學與金融分析等許多領域。然而，當底層資料產生機制在未知的時間點發生變化時，繼續監控該過程而不適應這種變化可能會導致檢測延遲或錯誤。雖然函數型資料的離線變點偵測已有相當多研究，線上方法仍相對有限。本文提出一套以離群分數為基礎的函數型資料線上變點偵測架構，結合資料深度、離群度資訊與序列監測概念，將不同形式的異常訊息轉換為可累積的監測證據。整體而言，本論文提供了一個具彈性與擴充性的函數型資料線上變點偵測框架，並顯示結合多種函數型的異常資訊有助於提升監測效能。

Functional data arise in many fields such as engineering monitoring, biomedical signal analysis, environmental science, and finance. However, when the underlying datagenerating mechanism changes at an unknown time point, continuing to monitor the process without adapting to the change may lead to delayed or incorrect detection. Although offline change-point detection for functional data has been widely studied, online procedures remain relatively limited. This thesis proposes an online change-point detection framework for functional data based on an outlier score. The proposed procedure combines data depth, outlyingness, and sequential monitoring to accumulate abnormality information over time. Overall, this thesis provides a flexible framework for online change-point detection in functional data and demonstrates the benefit of combining multiple forms of functional abnormality information.