Efficient hyperkernel learning using second-order cone programming

IEEE Transactions on Neural Networks
Ivor W Tsang, James T Kwok

Abstract

The kernel function plays a central role in kernel methods. Most existing methods can only adapt the kernel parameters or the kernel matrix based on empirical data. Recently, Ong et al. introduced the method of hyperkernels which can be used to learn the kernel function directly in an inductive setting. However, the associated optimization problem is a semidefinite program (SDP), which is very computationally expensive, even with the recent advances in interior point methods. In this paper, we show that this learning problem can be equivalently reformulated as a second-order cone program (SOCP), which can then be solved more efficiently than SDPs. Comparison is also made with the kernel matrix learning method proposed by Lanckriet et aL Experimental results on both classification and regression problems, with toy and real-world data sets, show that our proposed SOCP formulation has significant speedup over the original SDP formulation. Moreover, it yields better generalization than Lanckriet et al.'s method, with a speed that is comparable, or sometimes even faster, than their quadratically constrained quadratic program (QCQP) formulation.

References

Jul 25, 2000·Neural Computation·B ScholkopfP L Bartlett
Jul 7, 2001·Neural Computation·B SchölkopfR C Williamson
Sep 24, 2004·IEEE Transactions on Neural Networks·Martin M S LeeDennis DeCoste
Mar 25, 2005·IEEE Transactions on Neural Networks·Huilin XiongM Omair Ahmad
Feb 6, 2008·IEEE Transactions on Neural Networks·J T Kwok

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Citations

Mar 29, 2011·Neural Networks : the Official Journal of the International Neural Network Society·Ling JianChuanhou Gao
Jul 17, 2014·IEEE Transactions on Neural Networks and Learning Systems·Yuichi Motai
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Xinxing XuDong Xu
Feb 7, 2007·IEEE Transactions on Neural Networks·Dit-Yan Yeung, Hong Chang
Apr 4, 2009·IEEE Transactions on Neural Networks·Mingqing HuJames Tin-Yau Kwok
Mar 28, 2007·IEEE Transactions on Neural Networks·Zhiwei Shi, Min Han
Jan 25, 2011·IEEE Transactions on Neural Networks·Haiqin YangMichael R Lyu
Jun 11, 2008·IEEE Transactions on Neural Networks·Ioan BuciuIoannis Pitas

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