因為近年來「嚴重特殊傳染性肺炎」(COVID-19)病毒於全球蔓延，所以本研究欲進行醫療資料集分類，隨著資料特徵數量的提高，因此分類模型需要大量的運算成本，並且可能使分類模型陷入「維度詛咒」(curse of dimensionality)的問題，藉由「主成分分析法」(principal component analysis, PCA)，可有效進行維度縮減(Dimension reduction)，解決上述問題。

本研究提出一個基於「主成分」(Principal Components)與「反應變數」(Response Variable)相關性的特徵選取方法，透過「主成分分析」(principal component analysis, PCA)將原始相關性較高「屬性變數」的「屬性向量」轉換成任兩個互不相關的「主成分向量」，其目的在於消除「屬性變數」之間相關性太高時而導致的「多重共線性」(Multi-collinearity)問題。

分類模型的準確度(accuracy)可透過選取特徵以及反應變數之間的「複相關係數」(Squared Multiple Correlations, SMC)平方R^2進行判斷，先將主成分依「相關係數」(correlation coefficient)平方r^2排序，並依照Top 1、Top 2、Top3 … 的順序，逐步加入資料集中，因為主成分之間是互不相關的，所以可以透過r^2來累加計算R^2，我們決定使用r^2並非傳統主成分分析方法利用「變異量」(variance)來做為特徵選取的指標。

為了瞭解本研究所提出之特徵選取方法的效能，本研究使用「簡單貝氏分類器」(Naïve Bayes Classifier)對本研究所提出的特徵選取方法、依據變異量所選取的特徵以及依據「ROC曲線下面積」(area under the operating characteristic curve, AUC)的特徵選取方法，分別建立分類模型，再利用心臟病醫療資料集進行驗證，實驗結果顯示，本研究所提之特徵選取方法優於依據變異量特徵選取方法以及依據ROC曲線下面積(area under the operating characteristic curve, AUC)的特徵選取方法，有效減少特徵使用的數量，且分類模型準確度顯著提升。

Classification methods classify objects by exploring the relationship between the class and the features of the object.

Since the number of features is often large, classification becomes computationally intensive and therefore reducing the number of features needs to be addressed.

Principal component analysis (PCA) transforms coupled features into uncorrelated principal components. A subset of significant principal components is used for classification.

Traditional PCA ranks principal components by variances without considering the relationship between the individual principal component and the class variable.

A selection scheme based on the squared correlation between each individual principal component and the class variable is proposed to select significant principal components for classification.

Another selection scheme which ranks principal components by the area under the operating characteristic curve (AUC) corresponding to individual principal component is also investigated.

The proposed selection schemes used by the Naïve Bayes classifier are investigated on a heart disease dataset. Empirical results show the proposed selection scheme based on the squared correlations outperforms the traditional selection scheme based on the variances.

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