Prof Peter Andras P.Andras@napier.ac.uk
Dean of School of Computing Engineering and the Built Environment
High-dimensional function approximation with neural networks for large volumes of data
Andras, Peter
Authors
Abstract
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
Citation
Andras, P. (2018). High-dimensional function approximation with neural networks for large volumes of data. IEEE Transactions on Neural Networks and Learning Systems, 29(2), 500-508. https://doi.org/10.1109/TNNLS.2017.2651985
Journal Article Type | Article |
---|---|
Online Publication Date | Jan 25, 2017 |
Publication Date | 2018-02 |
Deposit Date | Nov 2, 2021 |
Journal | IEEE transactions on neural networks and learning systems |
Print ISSN | 2162-237X |
Publisher | Institute of Electrical and Electronics Engineers |
Peer Reviewed | Peer Reviewed |
Volume | 29 |
Issue | 2 |
Pages | 500-508 |
DOI | https://doi.org/10.1109/TNNLS.2017.2651985 |
Public URL | http://researchrepository.napier.ac.uk/Output/2808729 |
You might also like
A review of privacy-preserving federated learning for the Internet-of-Things
(2021)
Book Chapter
Amnesia: Neuropsychological Interpretation and Artificial Neural Network Simulation
(1998)
Journal Article
Neural activity pattern systems
(2004)
Journal Article
Medical research funding may have over-expanded and be due for collapse
(2005)
Journal Article
Downloadable Citations
About Edinburgh Napier Research Repository
Administrator e-mail: repository@napier.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search