<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is <italic>O</italic>(<italic>mn</italic>2). We consider algorithms with a complexity of <italic>O</italic>(<italic>mnl</italic>),where <italic>l&lt;n</italic> and <italic>l</italic> is often significantly smaller than <italic>n</italic>. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.</p></abstract>

The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is O(mn2). We consider algorithms with a complexity of O(mnl),where l<n and l is often significantly smaller than n. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.

A Fast Neural Network Learning Algorithm with Approximate Singular Value Decomposition

Department of Informatics, Faculty of Physics, Astronomy and Informatics

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to...

A Fast Neural Network Learning Algorithm with Approximate Singular Value Decomposition

Published Online: Sep 28, 2019

Page range: 581 - 594

Received: Sep 06, 2018

Accepted: Feb 22, 2019

DOI: https://doi.org/10.2478/amcs-2019-0043

Keywords
Moore–Penrose pseudo-inverse learning, radial basis function network, extreme learning machines, kernel methods, machine learning, singular value decomposition, deep extreme learning, principal component analysis

© 2019 Norbert Jankowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Fast Neural Network Learning Algorithm with Approximate Singular Value Decomposition

Published Online: Sep 28, 2019

Page range: 581 - 594

Received: Sep 06, 2018

Accepted: Feb 22, 2019

DOI: https://doi.org/10.2478/amcs-2019-0043

KeywordsMoore–Penrose pseudo-inverse learning, radial basis function network, extreme learning machines, kernel methods, machine learning, singular value decomposition, deep extreme learning, principal component analysis

© 2019 Norbert Jankowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Moore–Penrose pseudo-inverse learning, radial basis function network, extreme learning machines, kernel methods, machine learning, singular value decomposition, deep extreme learning, principal component analysis