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.

本文针对降维问题提出并分析了一种由序列化偏差估计、线性趋势估计和非线性残差估计组成的增量自编码器。实验结果表明，仅通过浅层网络封装非线性行为的自编码器能够识别具有低自编码误差的数据集的内在维度。该研究进一步比较了深层和浅层网络结构及其训练方法，发现深层网络结构在识别内在维度时获得较低的自编码误差，但是与浅层网络相比，检测到的维度并没有变化。