GREEDYKPCA |
Greedy Kernel Principal Component Analysis.
Synopsis:
model = greedykpca(X)
model = greedykpca(X,options)
Description:
This function implements a greedy kernel PCA algorithm.
The input data X are first approximated by GREEDYKPCA in the
feature space and second the ordinary PCA is applyed on the
approximated data. This algorithm has the same objective function
as the ordinary Kernel PCA but, in addition, the number of data in
the resulting kernel expansion is limited.
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:
X [dim x num_data] Input column vectors.
options [struct] Control parameters:
.ker [string] Kernel identifier. See 'help kernel' for more info.
.arg [1 x narg] Kernel argument.
.m [1x1] Maximal number of base vectors (Default m=0.25*num_data).
.p [1x1] Depth of search for the best basis vector (p=m).
.mserr [1x1] Desired mean squared reconstruction errors of approximation.
.maxerr [1x1] Desired maximal reconstruction error of approximation.
See 'help greedyappx' for more info about the stopping conditions.
.verb [1x1] If 1 then some info is displayed (default 0).
Output:
model [struct] Kernel projection:
.Alpha [nsv x new_dim] Multipliers defining kernel projection.
.b [new_dim x 1] Bias the kernel projection.
.sv.X [dim x num_data] Seleted subset of the training vectors..
.nsv [1x1] Number of basis vectors.
.kercnt [1x1] Number of kernel evaluations.
.MaxErr [1 x nsv] Maximal reconstruction error for corresponding
number of base vectors.
.MsErr [1 x nsv] Mean square reconstruction error for corresponding
number of base vectors.
Example:
X = gencircledata([1;1],5,250,1);
model = greedykpca(X,struct('ker','rbf','arg',4,'new_dim',2));
X_rec = kpcarec(X,model);
figure;
ppatterns(X); ppatterns(X_rec,'+r');
ppatterns(model.sv.X,'ob',12);
See also
KERNELPROJ, KPCA, GREEDYAPPX.
About: Statistical Pattern Recognition Toolbox
(C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
09-sep-2005, VF
19-feb-2005, VF
10-jun-2004, VF
05-may-2004, VF
14-mar-2004, VF