在此篇文章中，我們提出以密度函數比的方法分類的方法。Kanamori et al. (2009)提出利用最小平方法直接估計密度函數比的方法，並以其解決分類問題。然而，維度詛咒造成計算上的問題。為克服此問題，我們提出將資料投影到適當的維度下，再進行密度函數比的估計。我們以AUC做為評估分類的依據，模擬與實際資料都顯示我們的方法與羅吉斯回歸、SVM等方法可相比擬。另外，我們也以partial AUC作為評估分類的依據，結果亦呈現我們方法表現尚佳。

In this work, we consider a classification method based on density ratio estimation. Kanamori et al. (2009) proposed a direct estimation with least-squares approach for the density ratio estimation and showed how to use their density ration estimation approach for classification problem. However, the curse of the dimensionality would be caused the computational problem. To overcome this problem, we suggest projecting data into the proper subspace and then implement the density ratio estimation on this subspace instead of the whole data. We can choose to rotate data or basis. The latter is more efficient than the fronter. Simulation studies with different scenarios and several real examples are used to illustrate the performances of the proposed method. Based on the area under the receiver operating characteristic (ROC) curve (AUC) classification score, the results show the improvements of the proposed method and demonstrate the proposed method is comparable with other approaches, for example, logistic model approach. We also consider other classification score, partial AUC, the results presents that the proposed method performs fairly.

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