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Efficient hyperkernel learning using second-order cone programming.

Ivor Wai-hung Tsang1, James Tin-yau Kwok

  • 1Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. ivor@cs.ust.hk

IEEE Transactions on Neural Networks
|March 11, 2006
PubMed
Summary

This study reformulates hyperkernel learning from semidefinite programming (SDP) to second-order cone programming (SOCP). The new SOCP method offers significant speedups and improved generalization for kernel function learning.

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Area of Science:

  • Machine Learning
  • Optimization Theory

Background:

  • Kernel methods are central to machine learning, but adapting kernels is often limited to empirical data.
  • Hyperkernels allow direct inductive learning of kernel functions, but their optimization via semidefinite programming (SDP) is computationally intensive.

Purpose of the Study:

  • To reformulate the hyperkernel learning problem into a more computationally efficient optimization framework.
  • To improve the speed and generalization performance of inductive kernel learning.

Main Methods:

  • Reformulation of the hyperkernel learning problem from a semidefinite program (SDP) to a second-order cone program (SOCP).
  • Comparison of the proposed SOCP method with existing kernel matrix learning (Lanckriet et al.) and original SDP-based hyperkernel methods.

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Main Results:

  • The SOCP formulation provides a significant speedup compared to the original SDP formulation for hyperkernel learning.
  • The proposed method achieves better generalization performance than Lanckriet et al.'s kernel matrix learning approach.
  • The SOCP method demonstrates comparable or faster speeds than the quadratically constrained quadratic program (QCQP) formulation.

Conclusions:

  • The SOCP reformulation offers a more efficient and effective approach to inductive kernel learning.
  • This work advances the practical application of hyperkernels by addressing computational bottlenecks.