Multiple kernel learning: Difference between revisions

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{{short description|Set of machine learning methods}}

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:<math>\Theta=\frac{1}{\Pi} \sum^{\Pi}_{\pi=1}\sum^{M}_{m=1} D(q^{pi}_m(y|g^{\pi}_m(x))||p^{\pi}_m(f(x)|g^{\pi}_m(x)))</math>

where <math>D(Q||P)=\sum_iQ(i)\ln\frac{Q(i)}{P(i)}</math> is the [[Kullback–Leibler divergence]]. The combined minimization problem is optimized using a modified block gradient descent algorithm. For more information, see Wang et al.<ref>Wang, Shuhui et al. [httphttps://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6177671 S3MKL: Scalable Semi-Supervised Multiple Kernel Learning for Real-World Image Applications]. IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 14, NO. 4, AUGUST 2012</ref>

where <math>D(Q||P)=\sum_iQ(i)\ln\frac{Q(i)}{P(i)}</math> is the [[Kullback-Leibler divergence]].

The combined minimization problem is optimized using a modified block gradient descent algorithm. For more information, see Wang et al.<ref>Wang, Shuhui et al. [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6177671 S3MKL: Scalable Semi-Supervised Multiple Kernel Learning for Real-World Image Applications]. IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 14, NO. 4, AUGUST 2012</ref>

===Unsupervised learning===

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==Libraries==

Available MKL libraries include

* [httphttps://www.cs.cornell.edu/~ashesh/pubs/code/SPG-GMKL/download.html SPG-GMKL]: A scalable C++ MKL SVM library that can handle a million kernels.<ref>Ashesh Jain, S. V. N. Vishwanathan and Manik Varma. SPG-GMKL: Generalized multiple kernel learning with a million kernels. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Beijing, China, August 2012</ref>

* [http://research.microsoft.com/en-us/um/people/manik/code/GMKL/download.html GMKL]: Generalized Multiple Kernel Learning code in [[MATLAB]], does <math>\ell_1</math> and <math>\ell_2</math> regularization for supervised learning.<ref>M. Varma and B. R. Babu. More generality in efficient multiple kernel learning. In Proceedings of the International Conference on Machine Learning, Montreal, Canada, June 2009</ref>

* [https://archive.today/20141208195618/http://appsrv.cse.cuhk.edu.hk/~hqyang/doku.php?id=gmkl (Another) GMKL]: A different MATLAB MKL code that can also perform elastic net regularization<ref>Yang, H., Xu, Z., Ye, J., King, I., & Lyu, M. R. (2011). Efficient Sparse Generalized Multiple Kernel Learning. IEEE Transactions on Neural Networks, 22(3), 433-446</ref>