Discriminant Analysis for Dimensionality Reduction: An Overview of Recent Developments

Many biometric applications such as face recognition involve data with a large number of features [1–3]. Analysis of such data is challenging due to the curse-ofdimensionality [4, 5], which states that an enormous number of samples are required to perform accurate predictions on problems with a high dimensionality. Dimensionality reduction, which extracts a small number of features by removing irrelevant, redundant, and noisy information, can be an effective solution [6]. The commonly used dimensionality reduction methods include supervised approaches such as linear discriminant analysis (LDA) [7, 8], unsupervised ones such as principal component analysis (PCA) [9], and additional spectral and manifold learning methods [10–14]. When the class label information is available, supervised approaches, such as LDA, are usually more effective than unsupervised ones such as PCA for classification. Linear discriminant analysis (LDA) is a classical statistical approach for supervised dimensionality reduction and classification [8, 15–18]. LDA computes an optimal transformation (projection) by minimizing the within-class distance and maximizing the between-class distance simultaneously, thus achieving maximum