臺灣博碩士論文加值系統

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.

Acknowledgements i
Abstract ii
1 Introduction 1
1.1 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Robust Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . 3
2 Robustness of Linear Discriminant Analysis 4
2.1 Robust Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Measurement of Robustness . . . . . . . . . . . . . . . . . . . 5
2.1.2 M-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Robustness of Linear Discriminant Analysis . . . . . . . . . . . . . . 8
3 The Minimum γ-Divergence Estimation 12
4 γ-LDA Algorithm 16
4.1 Model Specification and Estimation . . . . . . . . . . . . . . . . . . . 17
4.2 Plug-in γ-LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 Projection Pursuit γ-LDA . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3.2 Projection Pursuit . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Simulation and Compression of γ-LDA . . . . . . . . . . . . . . . . . 23
5 Robustness of γ-LDA 29
6 Real Data 32
7 Discussion and Future Work 34

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