基於群集轉移行為的多重變異點分析

Abstract

本研究提出一種針對時序資料中多重變異點偵測的全新方法，結合密度式分群演算法與群集轉移行為之結構變化。藉由比較相鄰時間點的分群標籤變動，初步辨識變異點候選集合，再透過分群一致性指標（如RI與NMI）配合代表點篩選與肘點法，有效估計變異點數與位置。相較傳統方法，本方法具備無需預設分群數量、可自動排除雜訊觀測、並適用於非線性資料與受雜訊污染的資料等優勢。模擬實驗涵蓋多種場景，包括平均數平移、片段長度不等、狀態重複與高維稀疏變化等條件。本方法在多數場景中均展現高準確率與F-score，尤其在需定位精準且具解釋性之應用中具明顯優勢。與傳統CUSUM方法相較，能更有效避免過度偵測與誤判。整體而言，本方法為變異點偵測領域提供一具實用性與延展性之新方向。

We propose a novel unsupervised approach for multiple change point detection in time series based on cluster transition behavior. The method applies density-based clustering (DBSCAN) to reveal latent structure, identifies candidate change points via shifts in cluster assignments across time, and determines final change points using clustering consistency metrics such as RI and NMI, combined with representative selection and the elbow method. Unlike traditional approaches, our method does not require prior knowledge of the number of clusters, is robust to noise, and adapts well to non-linear data and data with noise. Extensive simulation studies demonstrate the method's strong performance across various scenarios, including mean shifts, unequal segment lengths, repeated states, and sparse high-dimensional changes. Our approach consistently achieves high accuracy and F-scores, particularly excelling in applications requiring precise localization and interpretability. Compared to classical methods like CUSUM, it effectively mitigates over-detection and false positives. Overall, this method offers a practical and extensible framework for robust change point detection.