Exploring nonlinear relationships in chemical data using kernel-based methods

Kernel methods, in particular support vector machines, have been further extended into a new class of methods, which could effectively solve nonlinear problems in chemistry by using simple linear transformation. In fact, the kernel function used in kernel methods might be regarded as a general protocol to deal with nonlinear data in chemistry. In this paper, the basic idea and modularity of kernel methods, together with some simple examples, are discussed in detail to give an in-depth understanding for kernel methods. Three key ingredients of kernel methods, namely dual form, nonlinear mapping and kernel function, provide a consistent framework of kernel-based algorithms. The modularity of kernel methods allows linear algorithms to combine with any kernel function. Thus, some commonly used chemometric algorithms are easily extended to their kernel versions.