Cluster-based Random Radial Basis Kernel Function for Hyperspectral Data Classification

Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in hyperspectral data classification due to its superior performance among other available kernel functions. Nonetheless, the cross-validation technique usually used for tunning the RBF parameter can be time-consuming and may result in sub-optimal values for the parameter. This paper proposed the cluster-based random radial basis function (CRRBF) kernel function as an alternative to the RBF kernel to achieve similar performance with a more manageable parameter, which is the number of clusters. The CRRBF kernel initially clusters the hyperspectral bands and then constructs an RBF kernel with a randomly assigned value as the kernel parameter from each cluster of bands. The final CRRBF kernel is constructed by adding up these basis RBF kernels. We have designed several experiments to evaluate the SVM performance trained with the CRRBF kernel considering a different number of clusters and training samples, using three hyperspectral data sets. The obtained results showed that the CRRBF kernel could provide comparable or better results than the RBF. The results also showed that the classification performance is pretty robust to the number of clusters, as the only open parameter of the CRRBF kernel.