nlpca Nonlinear principal component analysis (NLPCA)

Syntax

[pc, net] = nlpca(data, k)

pc = nlpca_get_components(net, data)
data_reconstruction = nlpca_get_data(net, pc)

Description

The nonlinear PCA is based on an auto-associative neural network (autoencoder), see also: www.nlpca.org .

pc = nlpca(data,k) extracts k nonlinear components from the data set. pc represents the estimated component values (scores).

net is a data structure explaining the neural network parameters for the nonlinear transformation from data space to component space and reverse.
net can be used in nlpca_get_components and nlpca_get_data to obtain component values (scores) for new data or reconstructed data for any component value.

Example

In this example nonlinear PCA (circular PCA) is applied to artificial data of a noisy circle.

   % generate circular data 
   t=linspace(-pi , +pi , 100);  % angular value t=-pi,...,+pi
   data = [sin(t);cos(t)];       % circle
   data = data + 0.2*randn(size(data));    % add noise

   % nonlinear PCA (circular PCA, inverse network architecture)
   [c,net]=nlpca(data, 1,  'type','inverse',  'circular','yes' );
                                
   % plot components             
   nlpca_plot(net)  
  

See also the demos of the toolbox below.

Download

The NLPCA toolbox is distributed under the GNU General Public License.
NLPCA can be downloaded as single package or individual files:

References

See also:

• Main page: NLPCA - Nonlinear PCA - auto-associative neural network
• Principal Component Analysis (PCA)
• PCA by using Matlab
• Independent Component Analysis (ICA)
• Complex Networks