Description: Nonlinear principal component analysis (NLPCA) based on auto-associative neural networks, also known as autoencoder, replicator networks, bottleneck or sandglass type networks.
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Nonlinear principal component analysis (NLPCA) is commonly seen as a nonlinear generalization of standard principal component analysis (PCA). It generalizes the principal components from straight lines to curves (nonlinear). Thus, the subspace in the original data space which is described by all nonlinear components is also curved. Nonlinear PCA can be achieved by using a neural network with an autoassociative architecture also known as autoencoder, replicator network, bottleneck or sandglass type network.
Here, NLPCA is applied to 19-dimensional spectral data representing equivalent widths of 19 absorption lines of 487 stars, available at www.cida.ve . The figure in the middle shows a visualisation of the data by using the first three components of standard PCA. Data of different colors belong to different spectral groups of stars. The first three components of linear PCA and of NLPCA are represented by grids in the left and right figure, respectively. Each grid represents the two-dimensional subspace given
see all publications: [ Matthias Scholz: publications ]