| BSVM2 | |
Multi-class BSVM with L2-soft margin.
Synopsis:
model = bsvm2( data, options )
Description:
This function trains the multi-class SVM classifier based
on BSVM formulation (bias added to the objective function) and
L2-soft margin penalization of misclassifications.
The quadratic programming task is optimized by one of the
following algorithms:
mdm ... Mitchell-Demyanov-Malozemov
imdm ... Mitchell-Demyanov-Malozemov Improved 1.
iimdm ... Mitchell-Demyanov-Malozemov Improved 2.
kozinec ... Kozinec algorithm.
keerthi ... NPA algorithm by Keerthi et al.
kowalczyk ... Based on Kowalczyk's maximal margin perceptron.
For more info refer to V.Franc: Optimization Algorithms for Kernel
Methods. Research report. CTU-CMP-2005-22. CTU FEL Prague. 2005.
ftp://cmp.felk.cvut.cz/pub/cmp/articles/franc/Franc-PhD.pdf .
Input:
data [struct] Training data:
.X [dim x num_data] Training vectors.
.y [1 x num_data] Labels (1,2,...,nclass).
options [struct] Control parameters:
.ker [string] Kernel identifier. See 'help kernel'.
.arg [1 x nargs] Kernel argument(s).
.C [1x1] Regularization constant.
.solver [string] Solver to be used: 'mdm', 'imdm' (default), 'iimdm',
'kozinec', 'kowalczyk','keerthi'.
.tmax [1x1] Maximal number of iterations (default inf).
.tolabs [1x1] Absolute tolerance stopping condition (default 0.0).
.tolrel [1x1] Relative tolerance stopping condition (default 0.001).
.thlb [1x1] Thereshold on the lower bound (default inf).
.cache [1x1] Number of columns of kernel matrix to be cached (default 1000).
.verb [1x1] If > 0 then some info is printed (default 0).
Output:
model [struct] Multi-class SVM classifier:
.Alpha [nsv x nclass] Weights.
.b [nclass x 1] Biases.
.sv.X [dim x nsv] Support vectors.
.nsv [1x1] Number of support vectors.
.options [struct] Copy of input options.
.t [1x1] Number of iterations.
.UB [1x1] Upper bound on the optimal solution.
.LB [1x1] Lower bound on the optimal solution.
.History [2 x (t+1)] UB and LB with respect to t.
.trnerr [1x1] Training classification error.
.kercnt [1x1] Number of kernel evaluations.
.cputime [1x1] CPU time (measured by tic-toc).
.stat [struct] Statistics about optimization:
.access [1x1] Number of requested columns of matrix H.
.t [1x1] Number of iterations.
.UB [1x1] Upper bound on the optimal value of criterion.
.LB [1x1] Lower bound on the optimal value of criterion.
.LB_History [1x(t+1)] LB with respect to t.
.UB_History [1x(t+1)] UB with respect to t.
.NA [1x1] Number of non-zero elements in solution.
Example:
data = load('pentagon');
options = struct('ker','rbf','arg',1,'C',10);
model = bsvm2(data,options )
figure;
ppatterns(data); ppatterns(model.sv.X,'ok',12);
pboundary(model);
See also
SVMCLASS, OAASVM, OAOSVM, GMNP.
About: Statistical Pattern Recognition Toolbox
(C) 1999-2005, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
09-sep-2005, VF
24-jan-2005, VF
29-nov-2004, VF
26-nov-2004, VF
16-Nov-2004, VF
31-may-2004, VF
23-jan-2003, VF