An Optimal Transformation for Discriminant and Principal Component Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
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
The FERET Evaluation Methodology for Face-Recognition Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Principal Manifolds and Probabilistic Subspaces for Visual Recognition
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
Face recognition using LDA mixture model
Pattern Recognition Letters
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Dimensionality Reduction via a Heteroscedastic Extension of LDA: The Chernoff Criterion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discriminative Common Vectors for Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parallel Image Matrix Compression for Face Recognition
MMM '05 Proceedings of the 11th International Multimedia Modelling Conference
Discriminant Analysis with Tensor Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Random Subspaces and Subsampling for 2-D Face Recognition
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Where Are Linear Feature Extraction Methods Applicable?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discriminant Analysis: A Least Squares Approximation View
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops - Volume 03
Multimodal oriented discriminant analysis
ICML '05 Proceedings of the 22nd international conference on Machine learning
Generalized Low Rank Approximations of Matrices
Machine Learning
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rapid and brief communication: Face recognition based on 2D Fisherface approach
Pattern Recognition
(2D)2LDA: An efficient approach for face recognition
Pattern Recognition
Journal of Cognitive Neuroscience
Rapid and brief communication: Two-dimensional FLD for face recognition
Pattern Recognition
2D-LDA: A statistical linear discriminant analysis for image matrix
Pattern Recognition Letters
GA-fisher: a new LDA-based face recognition algorithm with selection of principal components
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An optimization criterion for generalized discriminant analysis on undersampled problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face recognition by independent component analysis
IEEE Transactions on Neural Networks
Feature extraction based on Laplacian bidirectional maximum margin criterion
Pattern Recognition
A pre-clustering technique for optimizing subclass discriminant analysis
Pattern Recognition Letters
Maximum margin criterion with tensor representation
Neurocomputing
Feature extraction based on fuzzy 2DLDA
Neurocomputing
Block-wise 2D kernel PCA/LDA for face recognition
Information Processing Letters
Plant classification using leaf image based on 2D linear discriminant analysis
ICIC'10 Proceedings of the 6th international conference on Advanced intelligent computing theories and applications: intelligent computing
Contextual constraints based linear discriminant analysis
Pattern Recognition Letters
Computers and Electrical Engineering
Future Generation Computer Systems
Separable linear discriminant analysis
Computational Statistics & Data Analysis
Expert Systems: The Journal of Knowledge Engineering
Two-Dimensional locality discriminant projection for plant leaf classification
ICIC'12 Proceedings of the 8th international conference on Intelligent Computing Theories and Applications
Modular discriminant analysis and its applications
Artificial Intelligence Review
Hi-index | 0.01 |
Recent advances have shown that algorithms with (2D) matrix-based representation perform better than the traditional (1D) vector-based ones. In particular, 2D-LDA has been widely reported to outperform 1D-LDA. However, would the matrix-based linear discriminant analysis be always superior and when would 1D-LDA be better? In this paper, we investigate into these questions and have a comprehensive comparison between 1D-LDA and 2D-LDA in theory and in experiments. We analyze the heteroscedastic problem in 2D-LDA and formulate mathematical equalities to explore the relationship between 1D-LDA and 2D-LDA; then we point out potential problems in 2D-LDA. It is shown that 2D-LDA has eliminated the information contained in the covariance information between different local geometric structures, such as the rows or the columns, which is useful for discriminant feature extraction, whereas 1D-LDA could preserve such information. Interestingly, this new finding indicates that 1D-LDA is able to gain higher Fisher score than 2D-LDA in some extreme case. Furthermore, sufficient conditions on which 2D-LDA would be Bayes optimal for two-class classification problem are derived and comparison with 1D-LDA in this aspect is also analyzed. This could help understand how 2D-LDA is expected to achieve at its best, further discover its relationship with 1D-LDA, and well support other findings. After the theoretical analysis, comprehensive experimental results are reported by fairly and extensively comparing 1D-LDA with 2D-LDA. In contrast to the existing view that some 2D-LDA based algorithms would perform better than 1D-LDA when the number of training samples for each class is small or when the number of discriminant features used is small, we show that it is not always true and show that some standard 1D-LDA based algorithms could perform better in those cases on some challenging data sets.