Applied multivariate statistical analysis
Applied multivariate statistical analysis
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.)
Covariance pooling and stabilization for classification
Computational Statistics & Data Analysis
Covariance Matrix Estimation and Classification With Limited Training Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Quadratic Classifier Applied to Biometric Recognition
ECCV '02 Proceedings of the International ECCV 2002 Workshop Copenhagen on Biometric Authentication
Using Mixture Covariance Matrices to Improve Face and Facial Expression Recognitions
AVBPA '01 Proceedings of the Third International Conference on Audio- and Video-Based Biometric Person Authentication
Probabilistic Reasoning Models for Face Recognition
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Journal of Cognitive Neuroscience
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The quadratic discriminant (QD) classifier has proved to be simple and effective in many pattern recognition problems. However, it requires the computation of the inverse of the sample group covariance matrix. In many biometric problems, such as face recognition, the number of training patterns is considerably smaller than the number of features, and therefore the covariance matrix is singular. Several studies have shown that the use of mixture covariance matrices defined as a combination between the sample group covariance matrices and, for instance, the pooled covariance matrix, not only overcomes the singularity and instability of the sample group covariance matrices but also improves the QD classifier performance. However, little attention has been paid to understanding what has happened with the final shape of these mixture covariance matrices. In this work, we visually analyse in the commonly used eigenfaces space the eigenvectors and eigenvalues of these covariance matrices, given by the three following approaches: maximum likelihood, maximum classification accuracy, and maximum entropy. Experiments using the two well-known ORL and FERET face databases have shown that the maximum entropy approach is the one that achieves a more intuitive visual performance and best classification accuracies, especially in face experiments where moderate changes in facial expressions, pose, and scale, occur.