Matthias Scholz
Nonlinear PCA

Nonlinear PCA toolbox for MATLAB


Nonlinear principal component analysis (NLPCA)

Nonlinear PCA - Nonlinear principal component analysis (NLPCA)


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

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


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

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.


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             

See also the demos of the toolbox.

The NLPCA toolbox is distributed under the GNU General Public License.



Validation: Validation of nonlinear PCA.
Matthias Scholz
Neural Processing Letters, Volume 36, Number 1, Pages 21-30, 2012.
[ pdf (pre-print) | pdf (Neural Process Lett) | poster RECOMB 2012 | Matlab code]

review (book chapter): Nonlinear principal component analysis: neural network models and applications.
Matthias Scholz, Martin Fraunholz, and Joachim Selbig.
In Principal Manifolds for Data Visualization and Dimension Reduction, edited by Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, and Andrei Zinovyev. Volume 58 of LNCSE, pages 44-67. Springer Berlin Heidelberg, 2007.
[ pdf (all book chapters) | pdf (Springer) | entire book (Springer)]

Circular PCA: Analysing periodic phenomena by circular PCA.
Matthias Scholz.
In S. Hochreiter and R. Wagner, editors, Proceedings of the Conference on Bioinformatics Research and Development BIRD'07, LNCS/LNBI Vol. 4414, pages 38-47. Springer-Verlag Berlin Heidelberg, 2007.
[ pdf (final version at Springer) | pdf (author's pre-version)]

Inverse model, missing data: Non-linear PCA: a missing data approach.
Matthias Scholz, Fatma Kaplan, Charles L. Guy, Joachim Kopka, and Joachim Selbig.
Bioinformatics 21(20):3887-3895. 2005.
[ pdf (final version) | pdf (pre-version in colour) ]

Hierarchical NLPCA: Nonlinear PCA: a new hierarchical approach.
Matthias Scholz and Ricardo Vigário.
In M. Verleysen, editor, Proceedings ESANN. 2002.
[ pdf (pre-print version) | pdf (ESANN) ]

See also: