| KPCA | |
Kernel Principal Component Analysis.
Synopsis:
model = kpca(X)
model = kpca(X,options)
Description:
This function is implementation of Kernel Principal Component
Analysis (KPCA) [Schol98b]. The input data X are non-linearly
mapped to a new high dimensional space induced by prescribed
kernel function. The PCA is applied on the non-linearly mapped
data. The result is a model describing non-linear data projection.
See 'help kernelproj' for info how to project data.
Input:
X [dim x num_data] Training data.
options [struct] Decribes kernel and output dimension:
.ker [string] Kernel identifier (see 'help kernel');
(default 'linear').
.arg [1 x narg] kernel argument; (default 1).
.new_dim [1x1] Output dimension (number of used principal
components); (default num_data).
Output:
model [struct] Kernel projection:
.Alpha [num_data x new_dim] Multipliers.
.b [new_dim x 1] Bias.
.sv.X [dim x num_data] Training vectors.
.nsv [1x1] Number of training data.
.eigval [1 x num_data] Eigenvalues of centered kernel matrix.
.mse [1x1] Mean square representation error of maped data.
.MsErr [dim x 1] MSE with respect to used basis vectors;
mse=MsErr(new_dim).
.kercnt [1x1] Number of used kernel evaluations.
.options [struct] Copy of used options.
.cputime [1x1] CPU time used for training.
Example:
X = gencircledata([1;1],5,250,1);
model = kpca( X, struct('ker','rbf','arg',4,'new_dim',2));
XR = kpcarec( X, model );
figure;
ppatterns( X ); ppatterns( XR, '+r' );
See also
KERNELPROJ, PCA, GDA.
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:
2-jun-2008, VF, default new_dim changed to num_data; suggested by Claudio Lopez
4-may-2004, VF
10-july-2003, VF, computation of kercnt added
22-jan-2003, VF
11-july-2002, VF, mistake "Jt=zeros(N,L)/N" repared
(reported by SH_Srinivasan@Satyam.com).
5-July-2001, V.Franc, comments changed
20-dec-2000, V.Franc, algorithm was implemented