Efficient Kernel Discriminant Analysis via QR Decomposition

Linear Discriminant Analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications such as face recognition. Recently, a novel LDA algorithm based on QR Decomposition, namely LDA/QR, has been proposed, which is competitive in terms of classification accuracy with other LDA algorithms, but it has much lower costs in time and space. However, LDA/QR is based on linear projection, which may not be suitable for data with nonlinear structure. This paper first proposes an algorithm called KDA/QR, which extends the LDA/QR algorithm to deal with nonlinear data by using the kernel operator. Then an efficient approximation of KDA/QR called AKDA/QR is proposed. Experiments on face image data show that the classification accuracy of both KDA/QR and AKDA/QR are competitive with Generalized Discriminant Analysis (GDA), a general kernel discriminant analysis algorithm, while AKDA/QR has much lower time and space costs.