... command¹

On some systems, you may be required to specifiy the path with for instance ./trainmsvm .

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... parameter²

Note that MSVMpack implements the original formulation of each M-SVM, in which the complexity of the machine is tuned through a soft-margin parameter $C$ instead of a regularization constant $\lambda$ as described in [7].

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... updates³

A different setting is used for the CS model type as the dedicated working set selection method leads to a better use of the kernel cache. Thus, much less kernel evaluations are required and more threads can be used for gradient updates.

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... gradient⁴

See the function switch_thread() in libtrainMSVM.c for the parameters of these thread switches.

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... by⁵

The change in notation compared to [2] is due to the fact that MSVMpack solves the dual problem with respect to the variables $\alpha_{ik}$ instead of $\tau_{ik}= C\delta_{ik} - \alpha_{ik}$.

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... CLASS="sans">Spider⁶

http://people.kyb.tuebingen.mpg.de/spider/

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... CLASS="sans">BSVM⁷

http://www.csie.ntu.edu.tw/~cjlin/bsvm/

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... CLASS="sans">MCSVM⁸

http://www.cis.upenn.edu/~crammer/code-index.html

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... CLASS="sans">SMSVM⁹

http://www.stat.osu.edu/~ yklee/software.html

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... repository¹⁰

http://archive.ics.uci.edu/ml/datasets/Image+Segmentation

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... data¹¹

MNIST data sets are available at http://yann.lecun.com/exdb/mnist/. The data are originally stored as bytes, but the current implementation of the RBF kernel function in MSVMpack is faster with short integers than with bytes, so short integers are used in this experiment.

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... homepage¹²

http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/

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... repository¹³

http://archive.ics.uci.edu/ml/datasets/Letter+Recognition

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...lp_solve¹⁴

lp_solve is freely available under the terms of the GNU lesser general public license at http://lpsolve.sourceforge.net/.

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...mongoose¹⁵

mongoose is freely available under the terms of the GPL at http://code.google.com/p/mongoose/.

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