Linear Dimensionality Reduction via a Heteroscedastic Extension of LDA: The Chernoff Criterion

Authors:
Marco Loog;Robert P. W. Duin
Affiliations:
-;-
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2004

Citing 7
Cited 91

Introduction to statistical pattern recognition (2nd ed.)

Introduction to statistical pattern recognition (2nd ed.)
Elements of information theory

Elements of information theory
Statistical Pattern Recognition: A Review

IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria

IEEE Transactions on Pattern Analysis and Machine Intelligence
Toward Bayes-Optimal Linear Dimension Reduction

IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-iterative Heteroscedastic Linear Dimension Reduction for Two-Class Data

Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Optimal linear representations of images for object recognition

CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition

Where Are Linear Feature Extraction Methods Applicable?

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Feature Extraction for Multiclass Classification Problems Based on Class Mean and Covariance Discriminant Information

IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Weighted Metrics to Minimize Nearest-Neighbor Classification Error

IEEE Transactions on Pattern Analysis and Machine Intelligence
Subclass Discriminant Analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence
Breast cancer diagnosis using genetic programming generated feature

Pattern Recognition
Local Discriminant Wavelet Packet Coordinates for Face Recognition

The Journal of Machine Learning Research
Information Discriminant Analysis: Feature Extraction with an Information-Theoretic Objective

IEEE Transactions on Pattern Analysis and Machine Intelligence
A discriminant analysis using composite features for classification problems

Pattern Recognition
Automatic speech recognition and speech variability: A review

Speech Communication
Linear feature extraction by integrating pairwise and global discriminatory information via sequential forward floating selection and kernel QR factorization with column pivoting

Pattern Recognition
Approximate information discriminant analysis: A computationally simple heteroscedastic feature extraction technique

Pattern Recognition
Approximate information discriminant analysis: A computationally simple heteroscedastic feature extraction technique

Pattern Recognition
Metric learning by discriminant neighborhood embedding

Pattern Recognition
Optimizing the data-dependent kernel under a unified kernel optimization framework

Pattern Recognition
1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based?

Pattern Recognition
An extension of the Chernoff-based transformation matrix estimation method for on-line learning in Bayesian binary hypothesis tests

ISCGAV'07 Proceedings of the 7th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Linear dimensionality reduction by maximizing the Chernoff distance in the transformed space

Pattern Recognition
Feature extraction for one-class classification problems: Enhancements to biased discriminant analysis

Pattern Recognition
On Optimizing Subclass Discriminant Analysis Using a Pre-clustering Technique

CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Chernoff-Based Multi-class Pairwise Linear Dimensionality Reduction

CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
On Using Dimensionality Reduction Schemes to Optimize Dissimilarity-Based Classifiers

CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
A theoretical comparison of two-class Fisher's and heteroscedastic linear dimensionality reduction schemes

Pattern Recognition Letters
A minimax mutual information scheme for supervised feature extraction and its application to EEG-based brain-computer interfacing

EURASIP Journal on Advances in Signal Processing
Perturbation LDA: Learning the difference between the class empirical mean and its expectation

Pattern Recognition
An efficient discriminant-based solution for small sample size problem

Pattern Recognition
Linear Discriminant Analysis Using a Generalized Mean of Class Covariances and Its Application to Speech Recognition

IEICE - Transactions on Information and Systems
A Discriminant Analysis Method for Face Recognition in Heteroscedastic Distributions

ICB '09 Proceedings of the Third International Conference on Advances in Biometrics
Discriminative Shape Alignment

IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Heteroscedastic Probabilistic Linear Discriminant Analysis with Semi-supervised Extension

ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Learning a locality discriminating projection for classification

Knowledge-Based Systems
Audio-guided video-based face recognition

IEEE Transactions on Circuits and Systems for Video Technology
Linear boundary discriminant analysis

Pattern Recognition
A new discriminant analysis based on boundary/non-boundary pattern separation

IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction

Pattern Recognition
A novel Bayesian logistic discriminant model: An application to face recognition

Pattern Recognition
Generalized discriminant analysis: a matrix exponential approach

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Rapid and brief communication: Uncorrelated heteroscedastic LDA based on the weighted pairwise Chernoff criterion

Pattern Recognition
Linear dimensionality reduction using relevance weighted LDA

Pattern Recognition
A pre-clustering technique for optimizing subclass discriminant analysis

Pattern Recognition Letters
Multi-class pairwise linear dimensionality reduction using heteroscedastic schemes

Pattern Recognition
An adaptive nonparametric discriminant analysis method and its application to face recognition

ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
On using a pre-clustering technique to optimize LDA-based classifiers for appearance-based face recognition

CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
SVM-based feature extraction for face recognition

Pattern Recognition
Segmentation-driven offline handwritten Chinese and Arabic script recognition

SACH'06 Proceedings of the 2006 conference on Arabic and Chinese handwriting recognition
Robust linear dimensionality reduction for hypothesis testing with application to sensor selection

Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
MAP classifier with BDA features

FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 1
Incremental learning of LDA model for Chinese writer adaptation

Neurocomputing
Feature extraction based on subspace methods for regression problems

Neurocomputing
Computer-aided classification of zoom-endoscopical images using Fourier filters

IEEE Transactions on Information Technology in Biomedicine
Push-Pull marginal discriminant analysis for feature extraction

Pattern Recognition Letters
A conditional entropy minimization criterion for dimensionality reduction and multiple kernel learning

Neural Computation
Biological protein-protein interaction prediction using binding free energies and linear dimensionality reduction

PRIB'10 Proceedings of the 5th IAPR international conference on Pattern recognition in bioinformatics
A linear discriminant analysis method based on mutual information maximization

Pattern Recognition
Genetic-based minimum classification error mapping for accurate identifying Peer-to-Peer applications in the internet traffic

Expert Systems with Applications: An International Journal
An empirical evaluation on dimensionality reduction schemes for dissimilarity-based classifications

Pattern Recognition Letters
Optimized discriminative transformations for speech features based on minimum classification error

Pattern Recognition Letters
A novel SVM+NDA model for classification with an application to face recognition

Pattern Recognition
Input variable selection for feature extraction in classification problems

Signal Processing
A theoretical comparison of two linear dimensionality reduction techniques

CIARP'06 Proceedings of the 11th Iberoamerican conference on Progress in Pattern Recognition, Image Analysis and Applications
A new approach to multi-class linear dimensionality reduction

CIARP'06 Proceedings of the 11th Iberoamerican conference on Progress in Pattern Recognition, Image Analysis and Applications
Polynomial network classifier with discriminative feature extraction

SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
On optimizing kernel-based fisher discriminant analysis using prototype reduction schemes

SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
A fast fixed-point algorithm for two-class discriminative feature extraction

ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Pattern classification using composite features

ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Face recognition using heteroscedastic weighted kernel discriminant analysis

ICAPR'05 Proceedings of the Third international conference on Pattern Recognition and Image Analysis - Volume Part II
Conditional infomax learning: an integrated framework for feature extraction and fusion

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Extending kernel fisher discriminant analysis with the weighted pairwise chernoff criterion

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
A novel regularized fisher discriminant method for face recognition based on subspace and rank lifting scheme

ACII'05 Proceedings of the First international conference on Affective Computing and Intelligent Interaction
A novel fisher criterion based St-subspace linear discriminant method for face recognition

CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
Kernel discriminant analysis for regression problems

Pattern Recognition
A new linear dimensionality reduction technique based on chernoff distance

IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
A novel prototype reduction method for the K-nearest neighbor algorithm with K≥1

PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II
Using Clustering and Metric Learning to Improve Science Return of Remote Sensed Imagery

ACM Transactions on Intelligent Systems and Technology (TIST)
On the performance of chernoff-distance-based linear dimensionality reduction techniques

AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
Radar HRRP recognition based on discriminant information analysis

WSEAS Transactions on Information Science and Applications
Novel Fisher discriminant classifiers

Pattern Recognition
A boosting approach for supervised Mahalanobis distance metric learning

Pattern Recognition
Heteroscedastic linear feature extraction based on sufficiency conditions

Pattern Recognition
New class-dependent feature transformation for intrusion detection systems

Security and Communication Networks
Extended fisher criterion based on auto-correlation matrix information

SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Super-class Discriminant Analysis: A novel solution for heteroscedasticity

Pattern Recognition Letters
Evaluation of weighted Fisher criteria for large category dimensionality reduction in application to Chinese handwriting recognition

Pattern Recognition
FIDOS: A generalized Fisher based feature extraction method for domain shift

Pattern Recognition
Exploiting fisher and fukunaga-koontz transforms in chernoff dimensionality reduction

ACM Transactions on Knowledge Discovery from Data (TKDD)
Generalized mean for feature extraction in one-class classification problems

Pattern Recognition
The C-loss function for pattern classification

Pattern Recognition
Integrated Fisher linear discriminants: An empirical study

Pattern Recognition
Regularized discriminant entropy analysis

Pattern Recognition
Global plus local: A complete framework for feature extraction and recognition

Pattern Recognition
Semi-supervised linear discriminant analysis through moment-constraint parameter estimation

Pattern Recognition Letters
Graphical lasso quadratic discriminant function and its application to character recognition

Neurocomputing

Quantified Score

Hi-index	0.15

Visualization

Abstract

Abstract--We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chernoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chernoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented.