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NeuroCOLT
Technical Report NC-TR-02-121
2002-121
Optimizing Kernel Alignment over Combinations of Kernels
Jaz Kandola
John Shawe-Taylor
Nello Cristianini
ABSTRACT
Alignment has recently been proposed as a method for measuring the degree of
agreement between a kernel and a learning task \cite{cris2001}.
Previous approaches to optimizing kernel alignment have required the eigendecomposition of the
kernel matrix which can be computationally prohibitive especially for large kernel matrices.
In this paper we propose a general method for optimizing alignment over
a linear combination of kernels. We apply the approach to give both
transductive and inductive algorithms based on the Incomplete Cholesky factorization of the kernel matrix.
The Incomplete Cholesky factorization is equivalent to performing a Gram-Schmidt
orthogonalization of the training points in the feature space.
The alignment optimization method adapts the feature space to increase its training set alignment.
Regularization is required to ensure this alignment is also retained for the
test set. Both theoretical and experimental evidence is given to show that
improving the alignment leads to a reduction in generalization error
of standard classifiers.
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