Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Using Discriminant Eigenfeatures for Image Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix
Pattern Recognition Letters
Fractional-Step Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solving the Small Sample Size Problem of LDA
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 3 - Volume 3
Discriminative Common Vectors for Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Journal of Machine Learning Research
Computational and Theoretical Analysis of Null Space and Orthogonal Linear Discriminant Analysis
The Journal of Machine Learning Research
A comparison of generalized linear discriminant analysis algorithms
Pattern Recognition
A Gradient Linear Discriminant Analysis for Small Sample Sized Problem
Neural Processing Letters
Eigenfeature Regularization and Extraction in Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Bayes Optimality in Linear Discriminant Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Cancer classification by gradient LDA technique using microarray gene expression data
Data & Knowledge Engineering
Asymmetric Principal Component and Discriminant Analyses for Pattern Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new and fast implementation for null space based linear discriminant analysis
Pattern Recognition
Generalizing discriminant analysis using the generalized singular value decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
A two-stage linear discriminant analysis for face-recognition
Pattern Recognition Letters
A feature selection method using fixed-point algorithm for DNA microarray gene expression data
International Journal of Knowledge-based and Intelligent Engineering Systems
A feature selection method using improved regularized linear discriminant analysis
Machine Vision and Applications
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Null linear discriminant analysis (LDA) method is a popular dimensionality reduction method for solving small sample size problem. The implementation of null LDA method is, however, computationally very expensive. In this paper, we theoretically derive the null LDA method from a different perspective and present a computationally efficient implementation of this method. Eigenvalue decomposition (EVD) of S"T^+S"B (where S"B is the between-class scatter matrix and S"T^+ is the pseudoinverse of the total scatter matrix S"T) is shown here to be a sufficient condition for the null LDA method. As EVD of S"T^+S"Bis computationally expensive, we show that the utilization of random matrix together with S"T^+S"B is also a sufficient condition for null LDA method. This condition is used here to derive a computationally fast implementation of the null LDA method. We show that the computational complexity of the proposed implementation is significantly lower than the other implementations of the null LDA method reported in the literature. This result is also confirmed by conducting classification experiments on several datasets.