Toward an Optimal Supervised Classifier for the Analysis of Hyperspectral Data

This material is posted here with permission of the IEEE. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by sending a blank email message to pubspermissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. In this study we propose a supervised classifier based on implementation of the Bayes rule with kernels. The proposed technique first proposes an implicit nonlinear transformation of the data into a feature space seeking to fit normal distributions having a common covariance matrix onto the mapped data. One requirement of this approach is the evaluation of posterior probabilities. We express the discriminant function in dotproduct form, and then apply the kernel concept to efficiently evaluate the posterior probabilities. The proposed technique gives the flexibility required to model complex data structures that originate from a wide-range of class conditional distributions. Although we end up with piece-wise linear decision boundaries in the feature space, these corresponds to powerful nonlinear boundaries in the original input space. For the data we considered we have obtained some encouraging results