使用伽馬散度之穩健線性判別分析法

Abstract

線性判別分析可最大程度地提高組間差異與組內差異的比率，它被廣泛用於監督維度縮減中。在傳統的線性判別分析中，判別空間會被標籤錯誤的數據嚴重影響。為了克服這個問題，我們提出了基於伽馬散度的穩健線性判別分析。本文將介紹伽馬線性判別分析算法，並透過影響函數分析其穩健性。我們也藉由模擬資料與人臉辨識資料來展現新方法的優越性。

Linear discriminant analysis (LDA) which maximizes the ratio of the between-class variance to the within-class variance is widely used in supervised dimension reduction. In the traditional LDA, the discriminant space can be badly affected by the mislabeled data. To overcome this issue, we propose a robust linear discriminant analysis based on the γ-divergence which is a more robust measure than the Kullback-Leibler divergence. In this thesis, we will introduce the γ-LDA algorithm and analyze its robustness by the influence function. Furthermore, we will show the superior performance of γ-LDA on the simulated examples as well as face image data.