Editing Nonlinear dimensionality reduction (section)

=== Autoencoders ===

An [[autoencoder]] is a feed-forward [[neural network]] which is trained to approximate the identity function. That is, it is trained to map from a vector of values to the same vector. When used for dimensionality reduction purposes, one of the hidden layers in the network is limited to contain only a small number of network units. Thus, the network must learn to encode the vector into a small number of dimensions and then decode it back into the original space. Thus, the first half of the network is a model which maps from high to low-dimensional space, and the second half maps from low to high-dimensional space. Although the idea of autoencoders is quite old,<ref>{{cite book |last1=DeMers |first1=D. |last2=Cottrell |first2=G.W. |date=1993 |chapter=Non-linear dimensionality reduction |title=Advances in neural information processing systems |pages=580–7 |volume=5 |publisher= Morgan Kaufmann|isbn=1558600159 |oclc=928936290}}</ref> training of deep autoencoders has only recently become possible through the use of [[restricted Boltzmann machine]]s and stacked denoising autoencoders. Related to autoencoders is the [[NeuroScale]] algorithm, which uses stress functions inspired by [[multidimensional scaling]] and [[Sammon mapping]]s (see above) to learn a non-linear mapping from the high-dimensional to the embedded space. The mappings in NeuroScale are based on [[radial basis function network]]s.