  An additive autoencoder for dimension reduction, which is composed of a
serially performed bias estimation, linear trend estimation, and nonlinear
residual estimation, is proposed and analyzed. Computational experiments
confirm that an autoencoder of this form, with only a shallow network to
encapsulate the nonlinear behavior, is able to identify an intrinsic dimension
of a dataset with a low autoencoding error. This observation leads to an
investigation in which shallow and deep network structures, and how they are
trained, are compared. We conclude that the deeper network structures obtain
lower autoencoding errors during the identification of the intrinsic dimension.
However, the detected dimension does not change compared to a shallow network.
