自動合併可能性C迴歸分群演算法

Abstract

群集分析(Clustering Analysis)是一種很實用的統計分析方法，它透過邏輯程序將具有共同特性的資料聚集到同一群，使得群組內的個體相似性高，而不同群組間的個體相似性低。常見的應用包括機器學習(machine learning)、模型辨識(pattern recognition)及影像分析(image analysis)等。 混合迴歸(mixture regression)是群集分析重要的一環，而模糊分群是研究者常用的方法。傳統的模糊C迴歸(Fuzzy C-Regression；FCR)對初始值具有相當程度的依賴性，且容易受到離群值的影響。因此陸續有學者提出 Alpha截集模糊迴歸(α-cut Fuzzy C-Regression；α-cut FCR)、可能性C迴歸(Possibilistic C-Regression；PCR)等方法進行改善，使離群值的影響力變小，然而初始值的取以及資料群數的估計仍舊是PCR的兩大難題。 在本篇論文中，我們提出了一個新的自動合併可能性C迴歸(Automatic Merging Possibilistic C-Regression；AM-PCR)分群演算法，先透過階層式分群法(Hirearchical Clustering)選取初始值，搭配一種新型合併的方式，使得迴歸模型的參數估計更為穩健，並且在分群過程中，自動決定最適當的群數。

Cluster analysis is an useful statistical method grouping a set of objects which have common properties through logic programs; it makes objects in the same cluster similar to each other and those in different clusters dissimilar. Cluster analysis has been applied to machine learning, pattern recognition,image analysis, and many other fields. Mixture model is a vital branch of cluster analysis, and it is frequently analyzed by fuzzy clustering method. Traditional fuzzy c-regression (FCR) models depend heavily on initials and are sensitive to outliers; hence, several researches include α-cut fuzzy c-regression (α-cut FCR) and possibilistic c-regression (PCR) models were proposed to improve the weakness of FCR. However, the choice of initials and the estimation of cluster number are still difficult in mixture model analysis. In this paper, we proposed a new automatic merging possibilistic c-regression clustering algorithm; we choose initials by hirearchical clustering approach; we adopt a new type of merging approach to make the estimations for regression parameters more robust and determine the most suitable number of clusters automatically during implementation. The performance is discussed in comparison with traditional methods through simulation studies. The results demonstrate the superiority and usefulness of our proposed method.