Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Dimensionality reduction of highdimensional data with a nonLinear principal component aligned generative topographic mapping
 SIAM journal on scientific computing 36 (2014), Nr.3, S.A1027A1047 ISSN: 01965204 ISSN: 10648275 ISSN: 08857474 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
Abstract
Most highdimensional reallife data exhibit some dependencies such that data points do not populate the whole data space but lie approximately on a lowerdimensional manifold. A major problem in many data mining applications is the detection of such a manifold and the expression of the given data in terms of a moderate number of latent variables. We present a method which is derived from the generative topographic mapping (GTM) and can be seen as a nonlinear generalization of the principal component analysis (PCA). It can detect certain nonlinearities in the data but does not suffer from the curse of dimensionality with respect to the latent space dimension as the original GTM and thus allows for higher embedding dimensions. We provide experiments that show that our approach leads to an improved data reconstruction compared to the purely linear PCA and that it can furthermore be used for classification.