TY - GEN
T1 - Regularization with Dot-product kernels
AU - Smola, Alex J.
AU - Óvári, Zoltán L.
AU - Williamson, Robert C.
PY - 2001
Y1 - 2001
N2 - In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.
AB - In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.
UR - http://www.scopus.com/inward/record.url?scp=84898955546&partnerID=8YFLogxK
M3 - Conference contribution
SN - 0262122413
SN - 9780262122412
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000
PB - Neural Information Processing Systems Foundation
T2 - 14th Annual Neural Information Processing Systems Conference, NIPS 2000
Y2 - 27 November 2000 through 2 December 2000
ER -