SimpleMKL. Multiple kernel learning (MKL) aims at simultaneously learning a kernel and the associated predictor in supervised learning settings. For the support vector machine, an efficient and general multiple kernel learning algorithm, based on semi-infinite linear programming, has been recently proposed. This approach has opened new perspectives since it makes MKL tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs numerous iterations for converging towards a reasonable solution. In this paper, we address the MKL problem through a weighted 2-norm regularization formulation with an additional constraint on the weights that encourages sparse kernel combinations. Apart from learning the combination, we solve a standard SVM optimization problem, where the kernel is defined as a linear combination of multiple kernels. We propose an algorithm, named SimpleMKL, for solving this MKL problem and provide a new insight on MKL algorithms based on mixed-norm regularization by showing that the two approaches are equivalent. We show how SimpleMKL can be applied beyond binary classification, for problems like regression, clustering (one-class classification) or multiclass classification. Experimental results show that the proposed algorithm converges rapidly and that its efficiency compares favorably to other MKL algorithms. Finally, we illustrate the usefulness of MKL for some regressors based on wavelet kernels and on some model selection problems related to multiclass classification problems.

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  1. Gondzio, Jacek; González-Brevis, Pablo; Munari, Pedro: Large-scale optimization with the primal-dual column generation method (2016)
  2. Jawanpuria, Pratik; Nath, Jagarlapudi Saketha; Ramakrishnan, Ganesh: Generalized hierarchical kernel learning (2015)
  3. Althloothi, Salah; Mahoor, Mohammad H.; Zhang, Xiao; Voyles, Richard M.: Human activity recognition using multi-features and multiple kernel learning (2014)
  4. Cawley, Gavin C.; Talbot, Nicola L.C.: Kernel learning at the first level of inference (2014)
  5. Kobayashi, Takumi: Kernel-based transition probability toward similarity measure for semi-supervised learning (2014)
  6. Kobayashi, Takumi: Low-rank bilinear classification: efficient convex optimization and extensions (2014)
  7. Pan, Binbin; Lai, Jianhuang; Shen, Lixin: Ideal regularization for learning kernels from labels (2014)
  8. Wiliem, Arnold; Sanderson, Conrad; Wong, Yongkang; Hobson, Peter; Minchin, Rodney F.; Lovell, Brian C.: Automatic classification of human epithelial type 2 cell indirect immunofluorescence images using cell pyramid matching (2014)
  9. Afkanpour, Arash; Szepesvári, Csaba; Bowling, Michael: Alignment based kernel learning with a continuous set of base kernels (2013)
  10. Diethe, Tom; Girolami, Mark: Online learning with (multiple) kernels: a review (2013)
  11. Gönen, Mehmet; Alpaydın, Ethem: Localized algorithms for multiple kernel learning (2013)
  12. Hoi, Steven C.H.; Jin, Rong; Zhao, Peilin; Yang, Tianbao: Online multiple kernel classification (2013)
  13. Michailidis, George; d’Alché-Buc, Florence: Autoregressive models for gene regulatory network inference: sparsity, stability and causality issues (2013)
  14. Picard, David; Thome, Nicolas; Cord, Matthieu: JKernelMachines: a simple framework for kernel machines (2013)
  15. Prasad, Yamuna; Biswas, K.K.: Fuzzy rough based regularization in generalized multiple kernel learning (2013)
  16. Wulff, Sharon; Ong, Cheng Soon: Analytic center cutting plane method for multiple kernel learning (2013)
  17. Zhao, Jinwei; Yan, Guirong; Feng, Boqin; Mao, Wentao; Bai, Junqing: An adaptive support vector regression based on a new sequence of unified orthogonal polynomials (2013)
  18. Chen, Zhen-Yu; Fan, Zhi-Ping; Sun, Minghe: A hierarchical multiple kernel support vector machine for customer churn prediction using longitudinal behavioral data (2012)
  19. Fauvel, M.; Chanussot, J.; Benediktsson, J.A.: A spatial-spectral kernel-based approach for the classification of remote-sensing images (2012)
  20. Filippone, M.; Marquand, A.F.; Blain, C.R.V.; Williams, S.C.R.; Mourão-Miranda, J.; Girolami, M.: Probabilistic prediction of neurological disorders with a statistical assessment of neuroimaging data modalities (2012)

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