Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A semidiscrete matrix decomposition for latent semantic indexing information retrieval
ACM Transactions on Information Systems (TOIS)
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
SIAM Journal on Matrix Analysis and Applications
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Feature extraction via generalized uncorrelated linear discriminant analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
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
SIAM Journal on Matrix Analysis and Applications
Generalized Discriminant Analysis Using a Kernel Approach
Neural Computation
Generalizing discriminant analysis using the generalized singular value decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Gene Selection for Microarray Data by a LDA-Based Genetic Algorithm
PRIB '08 Proceedings of the Third IAPR International Conference on Pattern Recognition in Bioinformatics
Induction of multiclass multifeature split decision trees from distributed data
Pattern Recognition
Pattern Recognition Letters
Intelligent Decision Technologies
Classification of speech dysfluencies with MFCC and LPCC features
Expert Systems with Applications: An International Journal
Weighted generalized kernel discriminant analysis using fuzzy memberships
WSEAS Transactions on Mathematics
WSEAS Transactions on Mathematics
Analysis of Correlation Based Dimension Reduction Methods
International Journal of Applied Mathematics and Computer Science - Issues in Advanced Control and Diagnosis
Classification of Speech Dysfluencies Using LPC Based Parameterization Techniques
Journal of Medical Systems
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Linear discriminant analysis (LDA) is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability. However, in undersampled problems where the number of data samples is smaller than the dimension of data space, it is difficult to apply LDA due to the singularity of scatter matrices caused by high dimensionality. In order to make LDA applicable, several generalizations of LDA have been proposed recently. In this paper, we present theoretical and algorithmic relationships among several generalized LDA algorithms and compare their computational complexities and performances in text classification and face recognition. Towards a practical dimension reduction method for high dimensional data, an efficient algorithm is proposed, which reduces the computational complexity greatly while achieving competitive prediction accuracies. We also present nonlinear extensions of these LDA algorithms based on kernel methods. It is shown that a generalized eigenvalue problem can be formulated in the kernel-based feature space, and generalized LDA algorithms are applied to solve the generalized eigenvalue problem, resulting in nonlinear discriminant analysis. Performances of these linear and nonlinear discriminant analysis algorithms are compared extensively.