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ICML
2004
IEEE

Learning with non-positive kernels

15 years 23 days ago
Learning with non-positive kernels
In this paper we show that many kernel methods can be adapted to deal with indefinite kernels, that is, kernels which are not positive semidefinite. They do not satisfy Mercer's condition and they induce associated functional spaces called Reproducing Kernel Krein Spaces (RKKS), a generalization of Reproducing Kernel Hilbert Spaces (RKHS). Machine learning in RKKS shares many "nice" properties of learning in RKHS, such as orthogonality and projection. However, since the kernels are indefinite, we can no longer minimize the loss, instead we stabilize it. We show a general representer theorem for constrained stabilization and prove generalization bounds by computing the Rademacher averages of the kernel class. We list several examples of indefinite kernels and investigate regularization methods to solve spline interpolation. Some preliminary experiments with indefinite kernels for spline smoothing are reported for truncated spectral factorization, Landweber-Fridman iterat...
Alexander J. Smola, Cheng Soon Ong, Stéphan
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2004
Where ICML
Authors Alexander J. Smola, Cheng Soon Ong, Stéphane Canu, Xavier Mary
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