# An Additive Autoencoder for Dimension Estimation

arXiv: https://arxiv.org/abs/2210.06773 · HTML: https://mlsanity.com/paper/2210.06773/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 79 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [N2D: (Not Too) Deep Clustering via Clustering the Local Manifold of an Autoencoded Embedding](https://mlsanity.com/paper/1908.05968/) (2019)
- [Supervised Dimensionality Reduction for Big Data](https://mlsanity.com/paper/1709.01233/) (2017)
- [Accurate Node Feature Estimation with Structured Variational Graph Autoencoder](https://mlsanity.com/paper/2206.04516/) (2022)
- [Establishing strong imputation performance of a denoising autoencoder in a wide range of missing data problems](https://mlsanity.com/paper/2004.02584/) (2020)
- [Estimation of Dimensions Contributing to Detected Anomalies with Variational Autoencoders](https://mlsanity.com/paper/1811.04576/) (2018)
- [Dimension Estimation Using Autoencoders](https://mlsanity.com/paper/1909.10702/) (2019)

## Built on by (most cited first, 3 of 3)

- [Towards Responsible and Trustworthy Educational Data Mining: Comparing Symbolic, Sub-Symbolic, and Neural-Symbolic AI Methods](https://mlsanity.com/paper/2504.00615/) (2025)
- [Deep Fast Machine Learning Utils: A Python Library for Streamlined Machine Learning Prototyping](https://mlsanity.com/paper/2409.09537/) (2024)
- [SOSAE: Self-Organizing Sparse AutoEncoder](https://mlsanity.com/paper/2507.04644/) (2025)

## Abstract (arXiv)

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.