Editing Nonlinear dimensionality reduction (section)

=== Nonlinear PCA ===

Nonlinear PCA (NLPCA) uses [[backpropagation]] to train a multi-layer perceptron (MLP) to fit to a manifold.<ref>{{cite journal |last1=Scholz |first1=M. |last2=Kaplan |first2=F. |last3=Guy |first3=C. L. |last4=Kopka |first4=J. |last5=Selbig |first5=J. |title=Non-linear PCA: a missing data approach |journal=Bioinformatics |volume=21 |issue=20 |pages=3887–95 |publisher=Oxford University Press |year=2005 |doi=10.1093/bioinformatics/bti634 |pmid=16109748 |doi-access=free |hdl=11858/00-001M-0000-0014-2B1F-2 |hdl-access=free }}</ref> Unlike typical MLP training, which only updates the weights, NLPCA updates both the weights and the inputs. That is, both the weights and inputs are treated as latent values. After training, the latent inputs are a low-dimensional representation of the observed vectors, and the MLP maps from that low-dimensional representation to the high-dimensional observation space.