Abstract: In this paper we consider the problem of semi-supervised kernel function learning.
We first propose a general regularized framework for learning a kernel matrix,
and then demonstrate an equivalence between our proposed kernel matrix learning
framework and a general linear transformation learning problem. Our result
shows that the learned kernel matrices parameterize a linear transformation kernel
function and can be applied inductively to new data points. Furthermore, our result
gives a constructive method for kernelizing most existing Mahalanobis metric
learning formulations. To make our results practical for large-scale data, we modify
our framework to limit the number of parameters in the optimization process.
We also consider the problem of kernelized inductive dimensionality reduction in
the semi-supervised setting. To this end, we introduce a novel method for this
problem by considering a special case of our general kernel learning framework
where we select the trace norm function as the regularizer. We empirically demonstrate
that our framework learns useful kernel functions, improving the k-NN classification
accuracy significantly in a variety of domains. Furthermore, our kernelized
dimensionality reduction technique significantly reduces the dimensionality
of the feature space while achieving competitive classification accuracies.
- Topics:
- Kernel Methods
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Citation
- Inductive Regularized Learning of Kernel Functions (pdf, software)
P. Jain, B. Kulis, I. Dhillon.
In Neural Information Processing Systems (NIPS), pp. 946-954, December 2010.
Bibtex: