多層判別分析及其應用

Abstract

費雪判別分析(Fisher Linear Discriminant Analysis)是一種常見的分類方法，透過將資料屬性線性組合後能同時極大化組間變異並極小化組內變異來分類資料。在本研究裡，我們提出了一種新的判別模型結構，類似樹狀結構，都是由上往下一層一層將資料分割，與樹狀結構不同的是，此模型每一層會將一些資料針對1或2個類別做出分類，並將尚未判別之資料留至下一層，此外，每一層可選擇多個屬性並利用費雪判別分析做線性組合。為了建構此判別模型，我們提供了有系統的屬性選擇和切點決定方法，除此之外，模型在加入新屬性時會考慮整體模型的效能來決定模型該如何成長，為了防止過度配適(over-fitting)，也提供了模型停止條件。最後，為了驗證此模型，我們利用了數個模擬案例及一個甲狀腺腫瘤良惡性判別之問題來測試，且會與傳統的費雪判別分析及分類與迴歸樹(Classification and regression trees)作比較，驗證此判別模型效能。

Fisher linear discriminant analysis is a common classification method. It classifies instances by a linear combination of attributes that simultaneously minimizes the differences within classes while maximizes the differences between classes. In this research, we propose a new classification method, which has a structure similar to the classification and regression trees (CART) , splitting instances layer by layer. The difference between this structure and CART is that this model classifies some instances into 1 or 2 classes in each layer with the unclassified instances left over to next layer for further classification. In addition, a linear combination of multiple attributes by the Fisher linear discriminant analysis can be selected as the classifier at each layer. In order to construct the classification method, we propose a systematic methodology to select relevant attributes and proper cutpoints. Addition of attributes into the model, will be evaluated by the full model’s performance to decide how the model grow. To avoid the over-fitting problem, we also propose a stopping criterion. To verify the model, we generate some simulation cases and use one real case to validate our model. The real case is “classification of thyroid nodules by quantitative features from ultrasound sonograph.” We will compare the new model’s result with the Fisher discriminant analysis and CART.