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Add cauchy kernel cookbook #4338

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merged 4 commits into from Jun 20, 2018
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vinx13
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@vinx13 vinx13 commented Jun 16, 2018

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@karlnapf
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Thanks for this!

As said a few times before, let's not have more kernel cookbooks (after this one) as we already have tons of them. Rather, we should have cookbooks for algorithms that haven't been described yet

Cauchy Kernel
=============

The cauchy kernel is derived from the Cauchy distribution :cite:`basak2008kernel`. It is a long-tailed kernel defined as
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Minor: pls start new sentences in a new line

The cauchy kernel is derived from the Cauchy distribution :cite:`basak2008kernel`. It is a long-tailed kernel defined as

.. math::
K(x,x') = \frac{1}{1+\frac{\| x-x' \|^2}{\sigma}}
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I would prefer a lowercase k, unless K is used elsewhere

@@ -96,6 +96,16 @@ Distance

examples/distance/**

Kernel
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oh wait, we didnt have kernels yet? ;)
Ok then this is quite good to have :)

@@ -163,3 +163,10 @@ @article{hyvarinen2000independent
pages={411--430},
year={2000}
}
@inproceedings{basak2008kernel
author={J. Basak},
booktitle={2008 19th International Conference on Pattern Recognition},
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is this really the best reference? where do you have it from? can't we use some of the references we already used (like the kernel book by schölkopf?)

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i found several links point to this paper, e.g https://github.com/gmum/pykernels/blob/c8afdc79a15197ad3be2a0db0118f5e948577f49/pykernels/regular.py#L132
and I've checked that paper, the author gave a definition of it in sec.3

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ok cool. When citing it, put [Section 3] in there (if possible)

booktitle={2008 19th International Conference on Pattern Recognition},
title={A least square kernel machine with box constraints},
year={2008},
pages={1-4},
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pls do proper references. These pages here are definitely not correct

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ICPR papers are not re-assigned a page number when they are published. This is based on the reference format provided in https://ieeexplore.ieee.org/document/4761717

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I see, maybe we can remove them then?


We create an instance of :sgclass:`CCauchyKernel`.

.. sgexample:: cauchy:create_kernel
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Could you talk about the fact that a distance is used for this kernel?

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ok from my side

@karlnapf
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I restarted windows since it was failing

@@ -167,6 +167,5 @@ @inproceedings{basak2008kernel
author={J. Basak},
booktitle={2008 19th International Conference on Pattern Recognition},
title={A least square kernel machine with box constraints},
year={2008},
pages={1-4},
year={2008}
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cool thx!

Did you render this locally (the html output) and check that it all works ?

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Yes it works

@karlnapf
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Alright, great! thanks!

@karlnapf karlnapf merged commit c870b67 into shogun-toolbox:develop Jun 20, 2018
ktiefe pushed a commit to ktiefe/shogun that referenced this pull request Jul 30, 2019
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2 participants