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solver for training linear SVM classifiers
FEATURES
- SVM solvers for training linear classifiers from large scale-data.
- Two-class and genuine multi-class SVM formulations.
- A stand alone application and MEX interface for Matlab.
- Optimized for features represented in by different data types:
sparse/dense, double/single precision, int8.
- Reads examples from SVM^light format.
- Parallelized version of the two-class SVM solver.
- Allows using different C for each training example (only for Matlab).
- Training translation invariant image classifier from virtual examples using LBP features.
- Functions for computing image features based on Local Binary Patterns (LBP).
PROBLEM FORMULATION
OCAS solver is currently implemented for training binary (two-class) and multi-class
SVM classifiers:
1. Binary case: OCAS solves the following unconstrained convex optimization task
W^*,W0^* = argmin 0.5*(W'*W+W0^2) + sum C(i)*max( 0, 1-y(i)*(W'*X(:,i)+W0*X0) )
W,W0 i=1:nData
where C [nData x 1] is the regularization constant for each example,
X [nDim x nData] are training feature vectors and y [nData x 1] are their
binary labels (+1/-1). The result are parameters W^* [nDim x 1], W0^* [1 x 1] of
the linear rule
f(X) = sign( X'*W + W0 )
2. Multi-class case: OCAS solves the following unconstrained convex optimization task
W^* = argmin 0.5*sum_y (W(:,y)'*W(:,y)) + C* sum max( (y~=y(i)) + (W(:,y) - W(:,y(i)))'*X(:,i))
W i=1:nData y
where C is the regularization constant, X [nDim x nData] are training feature
vectors and y [nData x 1] are their labels from 1 to Y. The result are
parameters W^* [nDim x Y] of the linear rule
f(X) = argmax X'*W(:,y)
y
AVAILABILITY
LIBOCAS can be downloaded from
http://cmp.felk.cvut.cz/~xfrancv/ocas/html/index.html
PLATFORMS
Developed and tested under GNU/Linux.
LICENSE
LIBOCAS is licensed under the GPL version 3 (cf. LICENSE).
REFERENCES
V. Franc, S. Sonnenburg. Optimized Cutting Plane Algorithm for Large-Scale Risk Minimization.
The Journal of Machine Learning Research (JMLR), vol. 10, pp. 2157--2192. October 2009.
http://jmlr.csail.mit.edu/papers/volume10/franc09a/franc09a.pdf
V. Franc, S. Sonnenburg. OCAS optimized cutting plane algorithm for Support Vector
Machines. In Proceedings of ICML. Omnipress, 2008.
http://cmp.felk.cvut.cz/~xfrancv/papers/Franc-OCAS-ICML08.pdf
S. Sonnenburg, V. Franc. COFFIN: A Computational Framework for Linear SVMs.
In Proceedings of the 27nd International Machine Learning Conference (ICML'10).
Haifa 2010.
http://cmp.felk.cvut.cz/~xfrancv/papers/Sonnenburg-COFFIN-ICML10.pdf
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