Online learning with kernels
Jyrki Kivinen, Alex Smola and Bob Williamson
IEEE Transactions on Signal Processing
Kernel-based algorithms such as support vector ma-
chines have achieved considerable success in various problems in
batch setting, where all of the training data is available in advance.
Support vector machines combine the so-called kernel trick with
the large margin idea. There has been little use of these methods in
an online setting suitable for real-time applications. In this paper,
we consider online learning in a reproducing kernel Hilbert space.
By considering classical stochastic gradient descent within a fea-
ture space and the use of some straightforward tricks, we develop
simple and computationally efficient algorithms for a wide range of
problems such as classification, regression, and novelty detection.
In addition to allowing the exploitation of the kernel trick in
an online setting, we examine the value of large margins for clas-
sification in the online setting with a drifting target. We derive
worst-case loss bounds, and moreover, we show the convergence of
the hypothesis to the minimizer of the regularized risk functional.
We present some experimental results that support the theory
as well as illustrating the power of the new algorithms for online