A note on downdating the Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Fast adaptive condition estimation
SIAM Journal on Matrix Analysis and Applications
A singular value decomposition updating algorithm for subspace tracking
SIAM Journal on Matrix Analysis and Applications
Adaptive condition estimation for bank-one updates of QR factorizations
SIAM Journal on Matrix Analysis and Applications
Updating a rank-revealing ULV decomposition
SIAM Journal on Matrix Analysis and Applications
Updating URV decompositions in parallel
Parallel Computing
Block Downdating of Least Squares Solutions
SIAM Journal on Matrix Analysis and Applications
Accurate Downdating of Least Squares Solutions
SIAM Journal on Matrix Analysis and Applications
Perturbation analysis for block downdating of a Cholesky decomposition
Numerische Mathematik
The nature of statistical learning theory
The nature of statistical learning theory
Matrix computations (3rd ed.)
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Updating a Generalized URV Decomposition
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Machine learning and bioinformatics
Machine learning and bioinformatics
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
SMO'06 Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization
Softdoublemaxminover: perceptron-like training of support vector machines
IEEE Transactions on Neural Networks
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Kernelized nonlinear extensions of Fisher's discriminant analysis, discriminant analysis based on generalized singular value decomposition (LDA/GSVD), and discriminant analysis based on the minimum squared error formulation (MSE) have recently been widely utilized for handling undersampled high-dimensional problems and nonlinearly separable data sets. As the data sets are modified from incorporating new data points and deleting obsolete data points, there is a need to develop efficient updating and downdating algorithms for these methods to avoid expensive recomputation of the solution from scratch. In this paper, an efficient algorithm for adaptive linear and nonlinear kernel discriminant analysis based on regularized MSE, called adaptive KDA/RMSE, is proposed. In adaptive KDA/RMSE, updating and downdating of the computationally expensive eigenvalue decomposition (EVD) or singular value decomposition (SVD) is approximated by updating and downdating of the QR decomposition achieving an order of magnitude speed up. This fast algorithm for adaptive kernelized discriminant analysis is designed by utilizing regularization techniques and the relationship between linear and nonlinear discriminant analysis and the MSE. In addition, an efficient algorithm to compute leave-one-out cross validation is also introduced by utilizing downdating of KDA/RMSE.