An Additive Autoencoder for Dimension Estimation
This is an incremental improvement for researchers in dimension reduction, focusing on autoencoder structures for intrinsic dimension estimation.
The authors tackled the problem of intrinsic dimension estimation using an additive autoencoder composed of bias, linear trend, and nonlinear residual estimation, finding that deeper networks achieve lower autoencoding errors but do not change the detected dimension compared to shallow networks.
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.