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<title>LIBOCAS - Library implementing OCAS solver</title>
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<H2>LIBOCAS - Library implementing OCAS solver <br>for training linear SVM
classifiers from large-scale data</H2>
<A href="http://cmp.felk.cvut.cz/~xfrancv/">Vojtech Franc</a>,
<A href="http://ida.first.fraunhofer.de/homepages/sonne/first/">Soeren
Sonnenburg</a>
<p>
Last Modified: 23-Jul-2012
</div>
<hr>
<h4>Introduction</h4>
<p>
The library implements Optimized Cutting Plane Algorithm (OCAS)
for training linear SVM classifiers from large-scale data.
The computational effort of OCAS scales with O(m log m) where m is the sample size.
In an extensive empirical evaluation OCAS significantly outperforms current
state of the art SVM solvers, like SVM^light, SVM^perf and BMRM, achieving
speedups of over 1,000 on some datasets over SVM^light and 20 over SVM^perf,
while obtaining the same precise Support Vector solution. OCAS even in the early
optimization steps shows often faster convergence than the so far in this domain
prevailing approximative methods SGD and Pegasos. Effectively parallelizing
OCAS we were able to train on a dataset of size 15 million examples
(itself about 32GB in size) in just 671 seconds --- a competing string kernel SVM
required 97,484 seconds to train on 10 million examples sub-sampled from this
dataset.
<p>
<img align="top" border="0" src="new.gif">The library also implements COFFIN framework for
efficient training of translation invariant image classifiers from virtual
examples. As an example, we used the implemented framework to train a linear SVM
on a gender classification dataset of almost 5 million images on a plain
notebook with just 4GB of memory.
<h4>Features</h4>
<ul>
<li>SVM solvers for training linear classifiers from large scale-data.</li>
<li>Two-class and genuine multi-class SVM formulations.</li>
<li>A stand alone application and MEX interface for Matlab.</li>
<li>Optimized for features represented by different data types: sparse/dense, double/single precision, int8.</li>
<li>Allows training two-class SVM classifier with additional constraints enforcing a subset of selected weights to be non-negative.</li>
<li>Reads examples from SVM^light format.</li>
<li>Parallelized version of the two-class SVM solver.</li>
<li>Allows using different C for each training example (only for Matlab).</li>
<li>Training translation invariant image classifier from virtual examples using LBP features.</li>
<li>Functions for computing image features based on Local Binary Patterns (LBP).</li>
</ul>
<h4>Problem formulation</h4>
OCAS solver is currently implemented for training binary (two-class) and multi-class
SVM classifiers:
<p><b>1. Binary classification problem:</b> OCAS solves the following unconstrained convex optimization task
<div align="center">
<img align="top" vspace="2" src="linear_svm_sc.png">
</div>
where <img align="top" src="C_sc.png"> is the regularization constant and
<img align="top" border="0" src="trn_set_sc.png"> are training examples. The result is
the parameter vector <img align="top" border="0" src="w_sc.png"> of the linear rule
<img align="top" border="0" src="lin_rule_sc.png">
which assigns vector <img align="top" border="0" src="x_sc.png"> a class label +1 and/or -1.
<p><b>2. Multi-class classification probem:</b> OCAS solves the following unconstrained convex optimization task
<div align="center">
<img align="top" vspace="2" src="multi_linear_svm_sc.png">
</div>
where <img align="top" src="C_sc.png"> is the regularization constant,
<img align="top" border="0" src="set_y_sc.png"> is a finite set of labels and
<img align="top" border="0" src="multi_trn_set_sc.png"> are training
examples. The result is a set of parameter vectors <img align="top"
border="0" src="multi_w_sc.png"> of the linear rule
<img align="top" border="0" src="multi_lin_rule_sc.png">
which assigns vector <img align="top" border="0" src="x_sc.png"> a class label
from <img align="top" border="0" src="set_y_sc.png">.
<h4>Download</h4>
LIBOCAS can be downloaded from here:
<ul>
<li><img align="top" border="0" src="new.gif"> Version 0.97, 2013-05-14, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v097.zip">libocas_v097.zip</a>: Bug in makefile fixed. </li>
<!-- ------>
<li>Version 0.96, 2012-07-23, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v096.zip">libocas_v096.zip</a>: New solver which enforses a subset of selected weights to be non-negative
</li>
<li>Version 0.95, 2012-02-06, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v095.zip">libocas_v095.zip</a>: Support for features in single precision floats. Code polished. </li>
<li>Version 0.94, 2011-12-22, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v094.zip">libocas_v094.zip</a>: Support for features represented as int8. </li>
<li>Version 0.93, 2010-06-11, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v093.zip">libocas_v093.zip</a> </li>
<li>Version 0.92, 2008-08-03, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v092.zip">libocas_v092.zip</a> </li>
<li>Version 0.91, 2008-07-14, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v091.zip">libocas_v091.zip</a> </li>
<li>Version 0.90, 2008-10-12, <a
href="http://cmp.felk.cvut.cz/~xfrancv/ocas/libocas_v09.zip">libocas_v09.zip</a> </li>
</ul>
<h4><a href="ChangeLog">Change Log</a></h4>
<h4>Platforms</h4>
GNU/Linux.
<h4>Licensing Information</h4>
LIBOCAS is licensed under the GPL version 3.
<h4>References</h4>
<ul>
<li>S. Sonnenburg, V. Franc. <b>COFFIN: A Computational Framework for Linear SVMs.</b>
<i> In Proceedings of ICML.</i> Haifa, 2010.
[<a href="http://cmp.felk.cvut.cz/~xfrancv/papers/Sonnenburg-COFFIN-ICML10.pdf">pdf</a>]</li>
<li>V. Franc, S. Sonnenburg. <b>Optimized Cutting Plane Algorithm for Large-Scale
Risk Minimization. </b> <i>The Journal of Machine Learning Research (JMLR)</i>,
vol. 10, pp. 2157--2192. October 2009. [<a href="http://jmlr.csail.mit.edu/papers/volume10/franc09a/franc09a.pdf">pdf</a>]</li>
<li>V. Franc, S. Sonnenburg. <b>OCAS optimized cutting plane algorithm for Support Vector
Machines</b>. <i>In Proceedings of ICML</i>. Helsinki, 2008.
[<a href="http://cmp.felk.cvut.cz/~xfrancv/papers/Franc-OCAS-ICML08.pdf">pdf</a>]</li>
</ul>
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