An Optimal Transformation for Discriminant and Principal Component Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Uncorrelated Discriminant Analysis for Tissue Classification with Gene Expression Data
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An optimization criterion for generalized discriminant analysis on undersampled problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face recognition using kernel direct discriminant analysis algorithms
IEEE Transactions on Neural Networks
Efficient model selection for regularized linear discriminant analysis
CIKM '06 Proceedings of the 15th ACM international conference on Information and knowledge management
Adaptive dimension reduction using discriminant analysis and K-means clustering
Proceedings of the 24th international conference on Machine learning
Whitened LDA for face recognition
Proceedings of the 6th ACM international conference on Image and video retrieval
Supervised dimensionality reduction via sequential semidefinite programming
Pattern Recognition
A New Face Recognition Approach to Boosting the Worst-Case Performance
PCM '08 Proceedings of the 9th Pacific Rim Conference on Multimedia: Advances in Multimedia Information Processing
A new and fast implementation for null space based linear discriminant analysis
Pattern Recognition
A convex programming approach to the trace quotient problem
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Misalignment-robust face recognition
IEEE Transactions on Image Processing
Multilinear nonparametric feature analysis
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
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Dimensionality reduction is an important pre-processing step for many applications. Linear Discriminant Analysis (LDA) is one of the well known methods for supervised dimensionality reduction. However, the classical LDA formulation requires the nonsingularity of scatter matrices involved. For undersampled problems, where the data dimension is much larger than the sample size, all scatter matrices are singular and classical LDA fails. Many extensions, including null space based LDA (NLDA), orthogonal LDA (OLDA), etc, have been proposed in the past to overcome this problem. In this paper, we present a computational and theoretical analysis of NLDA and OLDA. Our main result shows that under a mild condition which holds in many applications involving high-dimensional data, NLDA is equivalent to OLDA. We have performed extensive experiments on various types of data and results are consistent with our theoretical analysis. The presented analysis and experimental results provide further insight into several LDA based algorithms.