Abstract
Over the past decade, kernel methods have gained much popularity in machine learning. Linear estimators have been popular due to their convenience in analysis and computation. However, nonlinear dependencies exist intrinsically in many real applications and are indispensable for effective modeling. Kernel methods can sometimes offer the best of both aspects. The reproducing kernel Hilbert space provides a convenient way to model nonlinearity, while the estimation is kept linear. Kernels also offer significant flexibility in analyzing generic non-Euclidean objects such as graphs, sets, and dynamic systems. Moreover, kernels induce a rich function space where functional optimization can be performed efficiently. Furthermore, kernels have also been used to define statistical models via exponential families or Gaussian processes and can be factorized by graphical models. Indeed, kernel methods have been widely used in almost all tasks in machine learning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Recommended Reading
Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68:337–404
Bach FR, Jordan MI (2002) Kernel independent component analysis. J Mach Learn Res 3:1–48
Boser B, Guyon I, Vapnik V (1992) A training algorithm for optimal margin classifiers. In: Haussler D (ed) Proceedings of annual conference on computational learning theory. ACM Press, Pittsburgh, pp 144–152
Collins M, Globerson A, Koo T, Carreras X, Bartlett P (2008) Exponentiated gradient algorithms for conditional random fields and max-margin markov networks. J Mach Learn Res 9:1775–1822
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge
Haussler D (1999) Convolution kernels on discrete structures. Technical report UCS-CRL-99-10, UC Santa Cruz
Hofmann T, Schölkopf B, Smola AJ (2008) Kernel methods in machine learning. Ann Stat 36(3):1171–1220
Lampert CH (2009) Kernel methods in computer vision. Found Trends Comput Graph Vis 4(3): 193–285
Poggio T, Girosi F (1990) Networks for approximation and learning. Proc IEEE 78(9):1481–1497
Schölkopf B, Smola A (2002) Learning with kernels. MIT Press, Cambridge
Schölkopf B, Smola AJ, Müller K-R (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299–1319
Schölkopf B, Tsuda K, Vert J-P (2004) Kernel methods in computational biology. MIT Press, Cambridge
Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge
Smola A, Vishwanathan SVN, Le Q (2007a) Bundle methods for machine learning. In: Koller D, Singer Y (eds) Advances in neural information processing systems, vol 20. MIT Press, Cambridge
Smola AJ, Gretton A, Song L, Schölkopf B (2007b) A Hilbert space embedding for distributions. In: International conference on algorithmic learning theory, Sendai. Volume 4754 of LNAI. Springer, pp 13–31
Smola AJ, Schölkopf B, Müller K-R (1998) The connection between regularization operators and support vector kernels. Neural Netw 11(5): 637–649
Steinwart I, Christmann A (2008) Support vector machines. Information science and statistics. Springer, New York
Taskar B, Guestrin C, Koller D (2004) Max-margin Markov networks. In: Thrun S, Saul L, Schölkopf B (eds) Advances in neural information processing systems, vol 16. MIT Press, Cambridge, pp 25–32
Vapnik V (1998) Statistical learning theory. Wiley, New York
Wahba G (1990) Spline models for observational data. Volume 59 of CBMS-NSF regional conference series in applied mathematics. SIAM, Philadelphia
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media New York
About this entry
Cite this entry
Zhang, X. (2017). Kernel Methods. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_144
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7687-1_144
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7685-7
Online ISBN: 978-1-4899-7687-1
eBook Packages: Computer ScienceReference Module Computer Science and Engineering