Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
The nature of statistical learning theory
The nature of statistical learning theory
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Learning over sets using kernel principal angles
The Journal of Machine Learning Research
A modified algorithm for generalized discriminant analysis
Neural Computation
IDR/QR: an incremental dimension reduction algorithm via QR decomposition
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Face Recognition by Using Discriminative Common Vectors
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Real-Time Face Recognition Using Gram-Schmidt Orthogonalization for LDA
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Discriminative Common Vectors for Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Discriminant Analysis Using a Kernel Approach
Neural Computation
Null space-based kernel fisher discriminant analysis for face recognition
FGR' 04 Proceedings of the Sixth IEEE international conference on Automatic face and gesture recognition
Face recognition using kernel direct discriminant analysis algorithms
IEEE Transactions on Neural Networks
Foley-Sammon optimal discriminant vectors using kernel approach
IEEE Transactions on Neural Networks
A rank-one update algorithm for fast solving kernel Foley-Sammon optimal discriminant vectors
IEEE Transactions on Neural Networks
Exploring similarity-based classification of larynx disorders from human voice
Speech Communication
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Generalized discriminant analysis (GDA) is the nonlinear extension of the classical linear discriminant analysis (LDA) via the kernel trick. Mathematically, GDA aims to solve a generalized eigenequation problem, which is always implemented by the use of singular value decomposition (SVD) in the previously proposed GDA algorithms. A major drawback of SVD, however, is the difficulty of designing an incremental solution for the eigenvalue problem. Moreover, there are still numerical problems of computing the eigenvalue problem of large matrices. In this article, we propose another algorithm for solving GDA as for the case of small sample size problem, which applies QR decomposition rather than SVD. A major contribution of the proposed algorithm is that it can incrementally update the discriminant vectors when new classes are inserted into the training set. The other major contribution of this article is the presentation of the modified kernel Gram-Schmidt (MKGS) orthogonalization algorithm for implementing the QR decomposition in the feature space, which is more numerically stable than the kernel Gram-Schmidt (KGS) algorithm. We conduct experiments on both simulated and real data to demonstrate the better performance of the proposed methods.