分層函數數據的集群研究

Abstract

函數數據反映隨時間演變的規律並提供豐富的資訊。為了滿足分析大量隨機函數樣本數據的需求，無監督集群方法變得愈來愈普及。由於廣泛的曲線數據處理和收集，許多數據集自然表現出層次結構。然而，關於多層次聚類的研究仍有待發展。因此，本研究旨在探討適用於多層次函數數據的集群方法。我們提出了多層次函數集群（MLFC）方法，在考慮平均值函數和共變異數函數差異的情況下，對第一層級和第二層級進行聚類。透過模擬研究，結果顯示出 MLFC 在多層次函數數據架構下的優越性能。此外，我們將 MLFC 應用於交通流量數據，識別出第一層和第二層集群中獨特的交通流量模式。我們的研究結果強調了 MLFC 在捕捉多層次函數數據模式方面的有效性。總體而言，MLFC 釋放了多層次函數數據的潛力，為深入分析和研究提供了有價值的見解和創新的研究方法。

Functional data offers valuable insights into evolution over time and provides rich information. The prevalence of unsupervised clustering methods has risen to meet the demand for analyzing large datasets of random function samples. Many datasets naturally exhibit hierarchical structures due to extensive curve data processing and collection. However, research on multilevel clustering is still in demand. This study addresses this gap by exploring clustering methods tailored for multilevel functional models. We propose a Multi-Level Functional Clustering (MLFC) approach, which clusters Level-1 and Level-2 units considering differentials in mean and covariance functions. The simulation study highlights MLFC's superior performance within multilevel functional frameworks. Applying MLFC to a traffic flow dataset identifies distinct traffic patterns at Level-1 and Level-2 clusters. Our findings underscore MLFC's effectiveness in capturing complex functional data patterns across multiple levels. Overall, MLFC unlocks the potential of multilevel functional data, providing valuable insights and innovative research methodologies.