Toward an optimal supervised classifier for the analysis of hyperspectral data

In this paper, 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 dot-product 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 piecewise 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.