Learning Algorithms for Quaternion-Valued Neural Networks

This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in...

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Bibliographic Details
Published in:Neural processing letters Vol. 47; no. 3; pp. 949 - 973
Main Author: Popa, Călin-Adrian
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2018
Springer Nature B.V
Subjects:
Algorithms
Approximation
Artificial Intelligence
Artificial neural networks
Back propagation
Calculus
Complex Systems
Computational Intelligence
Computer Science
Conjugate gradient method
Machine learning
Neural networks
Quaternions
Teaching methods
Time series
Quaternion-valued neural networks
Resilient backpropagation
SuperSAB
Levenberg–Marquardt algorithm
Conjugate gradient algorithms
Quickprop
Scaled conjugate gradient algorithm
Time series prediction
Quasi-Newton algorithms
Delta-bar-delta
ISSN:1370-4621, 1573-773X
Online Access:Get full text
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Summary:This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm.
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ISSN:1370-4621
1573-773X
DOI:10.1007/s11063-017-9716-1