# Some methods of constructing kernels in statistical learning

Discussiones Mathematicae Probability and Statistics (2010)

- Volume: 30, Issue: 2, page 179-201
- ISSN: 1509-9423

## Access Full Article

top## Abstract

top## How to cite

topTomasz Górecki, and Maciej Łuczak. "Some methods of constructing kernels in statistical learning." Discussiones Mathematicae Probability and Statistics 30.2 (2010): 179-201. <http://eudml.org/doc/277015>.

@article{TomaszGórecki2010,

abstract = {This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially $R^n$ and $S^n$. However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.},

author = {Tomasz Górecki, Maciej Łuczak},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {positive definite kernel; dot product kernel; statistical kernel; SVM; kPCA},

language = {eng},

number = {2},

pages = {179-201},

title = {Some methods of constructing kernels in statistical learning},

url = {http://eudml.org/doc/277015},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Tomasz Górecki

AU - Maciej Łuczak

TI - Some methods of constructing kernels in statistical learning

JO - Discussiones Mathematicae Probability and Statistics

PY - 2010

VL - 30

IS - 2

SP - 179

EP - 201

AB - This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially $R^n$ and $S^n$. However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.

LA - eng

KW - positive definite kernel; dot product kernel; statistical kernel; SVM; kPCA

UR - http://eudml.org/doc/277015

ER -

## References

top- [1] M. Abramowitz and I.A. Stegun, Chs. Legendre functions and orthogonal polynomials in Handbook of mathematical functions, Dover Publications, New York 1972.
- [2] B.E. Boser, I.M. Guyon and V.N. Guyon, A training algorithm for optimal margin classifiers, in D. Haussler, eds. 5th Annual ACM Workshop on COLT. ACM Press, Pittsburgh (1992), 144-152.
- [3] C.J.C. Burges, Geometry and invariance in kernel based methods in: Schölkopf, B. Burges, C.J.C. Smola, A.J. eds. Advances in kernel methods - support vector learning. MIT Press, Cambridge (1999), 89-116.
- [4] C. Cortes and V. Vapnik, Support-Vector Networks, Machine Learning 20 (1995), 273-297.
- [5] R. Herbrich, Learning Kernel Classifiers, MIT Press, London 2002. Zbl1063.62092
- [6] T. Hofmann, B. Schölkopf and A.J. Smola, Kernels methods in machine learning, Annals of Statistics 36 (2008), 1171-1220. Zbl1151.30007
- [7] Z. Ovari, Kernels, eigenvalues and support vector machines, Honours thesis, Australian National University, Canberra 2000.
- [8] B. Schölkopf and A.J. Smola, Learning with Kernels, MIT Press, London 2002.
- [9] B. Schölkopf, A.J. Smola and K.R. Müller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation 10 (1998), 1299-1319.
- [10] I.J. Schoenberg, Positive definite functions on spheres, Duke Mathematical Journal 9 (1942), 96-108. Zbl0063.06808
- [11] A. Tarantola, Inverse problem theory and methods for model paramenter estimation, SIAM, Philadelphia 2005. Zbl1074.65013
- [12] M. Zu, Kernels and ensembles: perspective on statistical learning, American Statistician 62 (2008), 97-109.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.