...SVMTorch¹

SVMTorch is available at http://www.idiap.ch/learning/SVMTorch.html.

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... case²

Note that this is the most common case. For instance for a Gaussian kernel with distinct examples x_i, it is easy to see that it is always the case.

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... ³

If we were really able to find such variables, this would mean that $(\boldsymbol{\alpha}, \boldsymbol{\alpha}^{\star})$ is a solution of our problem.

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... here.⁴

Note also that testing whether the $\alpha_i$and $\alpha_i^{\star}$ are non-zero at the same time would be a waste of time.

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... phase,⁵

This is verified in practice.

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... authors.⁶

For 5000 examples, we used -clever -best -lazy, while for more than 5000 examples, we used -clever -best -lazy -ssz 200.

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... dataset⁷

Available on http://www.cs.toronto.edu/~delve/data/kin/desc.html.

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... dataset⁸

Available on ftp://ftp.ics.uci.edu/pub/machine-learning-databases/covtype/covtype.info.

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... dataset⁹

Available on http://www.research.att.com/~yann/ocr/mnist/index.html.

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... kernel¹⁰

The kernel is $k(x,\, y) = \exp(-\Vert x -y\Vert^2 / \sigma^2)$.

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... projection¹¹

Actually, the original source code of this optimizer has been done by Leon Bottou.

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