Efficient sparse generalized multiple kernel learning

Haiqin Yang, Zenglin Xu, Jieping Ye, Irwin King, Michael R. Lyu

Research output: Contribution to journalArticlepeer-review

89 Scopus citations


Kernel methods have been successfully applied in various applications. To succeed in these applications, it is crucial to learn a good kernel representation, whose objective is to reveal the data similarity precisely. In this paper, we address the problem of multiple kernel learning (MKL), searching for the optimal kernel combination weights through maximizing a generalized performance measure. Most MKL methods employ the L1-norm simplex constraints on the kernel combination weights, which therefore involve a sparse but non-smooth solution for the kernel weights. Despite the success of their efficiency, they tend to discard informative complementary or orthogonal base kernels and yield degenerated generalization performance. Alternatively, imposing the Lp-norm (p < 1) constraint on the kernel weights will keep all the information in the base kernels. This leads to non-sparse solutions and brings the risk of being sensitive to noise and incorporating redundant information. To tackle these problems, we propose a generalized MKL (GMKL) model by introducing an elastic-net-type constraint on the kernel weights. More specifically, it is an MKL model with a constraint on a linear combination of the L1-norm and the squared L2-norm on the kernel weights to seek the optimal kernel combination weights. Therefore, previous MKL problems based on the L1-norm or the L2-norm constraints can be regarded as special cases. Furthermore, our GMKL enjoys the favorable sparsity property on the solution and also facilitates the grouping effect. Moreover, the optimization of our GMKL is a convex optimization problem, where a local solution is the global optimal solution. We further derive a level method to efficiently solve the optimization problem. A series of experiments on both synthetic and real-world datasets have been conducted to show the effectiveness and efficiency of our GMKL.

Original languageEnglish (US)
Article number5696759
Pages (from-to)433-446
Number of pages14
JournalIEEE Transactions on Neural Networks
Issue number3
StatePublished - Mar 2011


  • Grouping effect
  • Kernel methods
  • level method
  • multiple Kernel learning

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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