Efficient Kernel Discriminant Analysis via QR Decomposition
Efficient Kernel Discriminant Analysis via QR Decomposition
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发表时间：
2004-12
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通讯作者：
T. Xiong;Jieping Ye;Qi Li;Ravi Janardan;V. Cherkassky
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作者：
T. Xiong;Jieping Ye;Qi Li;Ravi Janardan;V. Cherkassky
线性判别分析（LDA）是一种众所周知的特征提取和降维方法。它已被广泛应用于人脸识别等许多应用中。近年来，提出了一种基于QR分解的新型LDA算法，即LDA/QR，该算法在分类精度上与其他LDA算法具有一定的竞争力，但在时间和空间上的成本要低得多。然而，LDA/QR基于线性投影，可能不适合具有非线性结构的数据。本文首先提出了一种KDA/QR算法，它将LDA/QR算法扩展到利用核算子处理非线性数据。在此基础上提出了KDA/QR的一种有效逼近方法——AKDA/QR。人脸图像数据实验表明，KDA/QR和AKDA/QR的分类精度与通用核判别分析算法GDA （Generalized Discriminant Analysis）相竞争，而AKDA/QR的时间和空间成本更低。
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.