聚類分析是用來預先瀏覽數據結構常見的方法，應用的領域像是在機器學習、圖像識 別和生態學研究都是常見的。大多數無監督學習的聚類方法，像是EM演算法和NEM演 算法，都是基於近似混合概似比以及需要預先給定聚類數而發展。此外，NEM演算法的 準確性對初始值的指定十分敏感，而且在矩陣計算中容易出現反矩陣不存在的問題，尤 其是對於在可視化中的三維數據集。本篇論文，提出了一種基於廣義學習的NEM(GLB- NEM)非監督式演算法，它不僅解決了初始值的敏感性和矩陣計算不存在的問題，而且 所提出的演算法能夠自動收斂到正確的分類群數。關於所提出的GLB-NEM聚類演算法的 統計推論在理論和模擬研究中都具有合理性。最後，本文透過兩筆實際資料分析說明方法 的實用性。;Cluster analysis is a common method to preview the underlying structure of the data in machine learning, image analysis, and ecological researches. Most of unsupervised learning clustering methods such as the EM algorithm and the NEM algorithm were developed based on the mixture likelihood ratio and the number of clusters needs to be specified in advance. In addition, the accuracy of the NEM method is sensitive to the specification of the initial value and it also suffers the singular issues in the computation of the matrix especially for the three-dimensional data sets. In this thesis, a generalized learning-based NEM (GLB- NEM) algorithm is proposed which not only solves the sensitivity of the initial value and the singular issues of the matrix, but also the proposed algorithm can automatically converge to the correct number of clusters. Statistical inferences about the proposed GLB-NEM cluster algorithm are justified both in theories and simulation studies. Also, two real data examples are analyzed for illustration.
