Exploring nonlinear relationships in chemical data using kernel-based methods

  • Cao D
  • Liang Y
  • Xu Q
 et al. 
  • 39

    Readers

    Mendeley users who have this article in their library.
  • 44

    Citations

    Citations of this article.

Abstract

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. © 2011 Elsevier B.V.

Author-supplied keywords

  • Dual solution
  • Kernel Fisher discriminant analysis (KFDA)
  • Kernel methods
  • Kernel partial least squares (KPLS)
  • Kernel principal component analysis (KPCA)
  • Support vector machines (SVMs)

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free