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2010 | 30 | 2 | 179-201
Tytuł artykułu

Some methods of constructing kernels in statistical learning

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Abstrakty
EN
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.
Twórcy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  • Department of Civil and Environmental Engineering, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland
Bibliografia
  • [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.
  • [6] T. Hofmann, B. Schölkopf and A.J. Smola, Kernels methods in machine learning, Annals of Statistics 36 (2008), 1171-1220.
  • [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.
  • [11] A. Tarantola, Inverse problem theory and methods for model paramenter estimation, SIAM, Philadelphia 2005.
  • [12] M. Zu, Kernels and ensembles: perspective on statistical learning, American Statistician 62 (2008), 97-109.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1127
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