CONF grandvalet:ICML-1:2007/IDIAP More Efficiency in Multiple Kernel Learning Rakotomamonjy, Alain Bach, Francis Canu, Stéphane Grandvalet, Yves EXTERNAL https://publications.idiap.ch/attachments/papers/2007/grandvalet-ICML-1-2007.pdf PUBLIC https://publications.idiap.ch/index.php/publications/showcite/grandvalet:rr07-18 Related documents International Conference on Machine Learning (ICML) 2007 IDIAP-RR 07-18 An efficient and general multiple kernel learning (MKL) algorithm has been recently proposed by \singleemcite{sonnenburg_mkljmlr}. This approach has opened new perspectives since it makes the MKL approach tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs several iterations before converging towards a reasonable solution. In this paper, we address the MKL problem through an adaptive 2-norm regularization formulation. Weights on each kernel matrix are included in the standard SVM empirical risk minimization problem with a $\ell_1$ constraint to encourage sparsity. We propose an algorithm for solving this problem and provide an new insight on MKL algorithms based on block 1-norm regularization by showing that the two approaches are equivalent. Experimental results show that the resulting algorithm converges rapidly and its efficiency compares favorably to other MKL algorithms. REPORT grandvalet:rr07-18/IDIAP More Efficiency in Multiple Kernel Learning Rakotomamonjy, Alain Bach, Francis Canu, Stéphane Grandvalet, Yves EXTERNAL https://publications.idiap.ch/attachments/reports/2007/grandvalet-idiap-rr-07-18.pdf PUBLIC Idiap-RR-18-2007 2007 IDIAP To appear in \textit{Proceedings of the $\mathit{24}^{th}$ International Conference on Machine Learning}, Corvallis, OR, 2007 An efficient and general multiple kernel learning (MKL) algorithm has been recently proposed by \singleemcite{sonnenburg_mkljmlr}. This approach has opened new perspectives since it makes the MKL approach tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs several iterations before converging towards a reasonable solution. In this paper, we address the MKL problem through an adaptive 2-norm regularization formulation. Weights on each kernel matrix are included in the standard SVM empirical risk minimization problem with a $\ell_1$ constraint to encourage sparsity. We propose an algorithm for solving this problem and provide an new insight on MKL algorithms based on block 1-norm regularization by showing that the two approaches are equivalent. Experimental results show that the resulting algorithm converges rapidly and its efficiency compares favorably to other MKL algorithms.