Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Linear Discriminant Analysis for Two Classes via Removal of Classification Structure
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Deterministic Annealing Approach for Parsimonious Design of Piecewise Regression Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interactive Linear Algebra with Maple V
Interactive Linear Algebra with Maple V
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Selecting the best hyperplane in the framework of optimal pairwise linear classifiers
Pattern Recognition Letters
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
Design of an automatic wood types classification system by using fluorescence spectra
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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
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 new multidimensional feature transformation for linear classifiers and its applications
MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
A new method for DNA microarray image segmentation
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
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
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Optimal Bayesian linear classifiers have been studied in the literature for many decades. In this paper, we demonstrate that all the known results consider only the scenario when the quadratic polynomial has coincident roots. Indeed, we present a complete analysis of the case when the optimal classifier between two normally distributed classes is pairwise and linear. To the best of our knowledge, this is a pioneering work for the use of such classifiers in any area of statistical Pattern Recognition (PR). We shall focus on some special cases of the normal distribution with nonequal covariance matrices. We determine the conditions that the mean vectors and covariance matrices have to satisfy in order to obtain the optimal pairwise linear classifier. As opposed to the state of the art, in all the cases discussed here, the linear classifier is given by a pair of straight lines, which is a particular case of the general equation of second degree. One of these cases is when we have two overlapping classes with equal means, which resolves the general case of the Minsky's paradox for the perceptron. We have also provided some empirical results, using synthetic data for the Minsky's paradox case, and demonstrated that the linear classifier achieves very good performance. Finally, we have tested our approach on real life data obtained from the UCI machine learning repository. The empirical results that we obtained show the superiority of our scheme over the traditional Fisher's discriminant classifier.