A framework of quasiconformal mapping-based kernel machine with its application to hyperspectral remote sensing

Kernel machine is a feasible and effective nonlinear feature extraction method on data analysis, for example, hyperspectral sensing data. Kernel trick improves largely the performance of learning system including recognition, clustering, prediction through the nonlinear kernel mapping from the input data space to output data space. The performance of kernel-based system is largely influenced by the function and parameter of kernel. Optimizing only the parameters is not effective to promote the kernel-based learning system, because the data distribution is not changed only changing the kernel parameter. Moreover, no any universal single kernel is very adaptive to all applications. We present a framework of quasiconformal mapping-based kernel learning machine under single kernel and multiple kernels for hyperspectral image data classification. The performance of learning system is improved largely owing to the two facts: quasiconformal kernel structure changes the data structure in the kernel empirical space; quasiconformal multikernels characterize precisely the data for improving performance on solving complex visual learning tasks. The learning framework is applied to the hyperspectral image classification, and some experiments are implemented on two hyperspectral image databases.