在人臉辨識中，線性判別分析法(Linear Discriminant Analysis，簡稱 LDA)經常遇到所謂的「小樣本」問題，也被稱為「維度災難」。當資料維度比訓練影像的數量大許多時，便會出現此問題。其中一種處理這種情況的方法是子空間線性判別分析法(Subspace LDA)，它包含兩個主要的步驟：首先使用主成分分析法(Principal Component Analysis，簡稱 PCA) 的概念降低維度，然後使用線性判別分析法的概念加以分類。在這篇論文中，我們探討四種子空間線性判別分析法： 「Fisherface」，「Complete PCA plus LDA」，「IDAface」和「BDPCA plus LDA」，並比較它們在處理人臉辨識小樣本問題的有效性。我們以三個公開的人臉資料庫，分別是：JAFFE、ORL及FEI，來作實驗。實驗結果顯示，對於處理人臉辨識小樣本問題，「BDPCA plus LDA」方法在這些子空間線性判別分析法中有最佳的表現。

In face recognition, LDA often encounters the so-called “small sample size” (SSS) problem, also known as “curse of dimensionality”. This problem occurs when the dimensionality of the data is quite large in comparison to the number of available training images. One of the approaches for handling this situation is the subspace LDA. It is a two-stage framework: it first uses PCA-based method for dimensionality reduction, and then LDA-based method is applied for classification. In this thesis, we investigate four popular subspace LDA methods: “Fisherface”, “complete PCA plus LDA”, “IDAface” and “BDPCA plus LDA” and compare their effectiveness when handling the SSS problem in face recognition. Extensive experiments have been performed on three publically available face databases: the JAFFE, ORL and FEI databases. Experimental results show that among the subspace LDA methods under investigation, the performance of the BDPCA plus LDA method is the best for solving the SSS problem in face recognition.

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