| PCA | |
Principal Component Analysis.
Synopsis:
model = pca(X)
model = pca(X,new_dim)
model = pca(X,var)
Description:
It computes Principal Component Analysis, i.e., the
linear transform which makes data uncorrelated and
minize the reconstruction error.
model = pca(X,new_dim) use to specify explicitely output
dimesnion where new_dim >= 1.
model = pca(X,var) use to specify a portion of discarded
variance in data where 0 <= var < 1. The new_dim is
selected be as small as possbile and to satisfy
var >= MsErr(new_dim)/MaxMsErr
where MaxMsErr = sum(sum(X.^2)).
Input:
X [dim x num_data] training data stored as columns.
new_dim [1x1] Output dimension; new_dim > 1 (default new_dim = dim);
var [1x1] Portion of discarded variance in data.
Ouputs:
model [struct] Linear projection:
.W [dim x new_dim] Projection matrix.
.b [new_dim x 1] Bias.
.eigval [dim x 1] eigenvalues.
.mse [real] Mean square representation error.
.MsErr [dim x 1] Mean-square errors with respect to number
of basis vectors; mse=MsErr(new_dim).
.mean_X [dim x 1] mean of training data.
Example:
in_data = load('iris');
model = pca(in_data.X, 2)
out_data = linproj(in_data,model);
figure; ppatterns(out_data);
See also
LINPROJ, PCAREC, KPCA.
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:
20-may-2004, VF
20-june-2003, VF
21-jan-03, VF
20-jan-03, VF
16-Jan-2003, VF, new comments.
26-jun-2002, VF