On the learning machine with quaternionic domain neural network and its high-dimensional applications
Pages 5189 - 5202
Abstract
There are various high-dimensional engineering and scientific applications in communication, control, robotics, computer vision, biometrics, etc.; where researchers are facing predicament to fabricate an intelligent and robust neural system which can process higher dimensional information efficiently. In various literatures, the conventional neural networks based only on real valued, are tried to solve the problem associated with high-dimensional parameters, but these neural network structures possess high complexity and are very time consuming and weak to noise. These networks are also not able to learn magnitude and phase values simultaneously in space. The quaternion is the number, which possesses the magnitude in all four directions and phase information is embedded within it. This paper presents a learning machine with a quaternionic domain neural network that can finely process magnitude and phase information of high dimension data without any hassle. The learning and generalization capability of the proposed learning machine is performed through chaotic time series predictions (Lorenz system and Chua’s circuit), 3D linear transformations, and 3D face recognition as benchmark problems, which demonstrate the significance of the work.
References
[1]
B.K. Tripathi, On the complex domain deep machine learning for face recognition, Applied Intelligence, Springer, 2016, ISSN: 0924-669X, DOI
[2]
B.K. Tripathi and P.K. Kalra, On efficient learning machine with root power mean neuron in complex domain, IEEE Transaction on Neural Networks 22(05) (2011), 727–738.
[3]
T. Nitta, An extension of the back-propagation algorithm to complex numbers, Neural Networks 10(8) (1997), 1391–1415.
[4]
T. Nitta, An analysis of the fundamental structure of complex-valued neurons, Neural Process 12 (2000), 239–246.
[5]
A. Hirose, Complex-valued neural networks. Springer-Verlag, New Yark, 2006.
[6]
M.K. Muezzinoglu, C. Guzelis and J.M. Zurada, A new design method for complex-valued multistate Hopfield associative memory, IEEE Transaction Neural Networks 14(4) (2003), 891–899.
[7]
B.K. Tripathi and P.K. Kalra, Complex generalized-mean neuron model and its applications, Applied Soft Computing, Elsevier Science 11(01) (2011), 768–777.
[8]
T. Nitta, 3D vector version of the back-propagation algorithm, Int Joint Conf on Neural Networks 2 (1992), 511–516.
[9]
B.K. Tripathi and P.K. Kalra, On the learning machine in three dimensional mapping, Neural Computing and Applications 20 (2011), 105–111.
[10]
B.K. Tripathi, High dimensional neurocomputing: Growth, appraisal and applications, Springer, London, 2014.
[11]
W.R. Hamilton, Lectures on quaternions. Hodges and Smith: Dublin, Ireland, 1853.
[12]
J.B. Kuipers, Quaternions and rotation sequences: A primer with applications to orbits, aerospace and virtual Reality. Princeton University Press: Princeton, NJ, USA, 1998.
[13]
S.G. Hoggar, Mathematics for computer graphics, Cambridge University Press: Cambridge, MA, USA, 1992.
[14]
T. Nitta, A quaternary version of the back-propagation algorithm, ICNN 5(1) (1995), 2753–2756.
[15]
T. Isokawa, H. Nishimura and N. Matsui, Quaternionic multilayer perceptron with local analyticity, Information 3 (2012), 756–770.
[16]
B.C. Ujang, C.C. Took and D.P. Mandic, Quaternion-valued nonlinear adaptive filtering, IEEE Transaction on Neural Networks 22(8) (2011), 1193–1206.
[17]
M. Wang, C.C. Took and D.P. Mandic, A class of fast quaternion valued variable stepsize stochastic gradient learning algorithms for vector sensor processes, IJCNN, 2011, pp. 2783–2786.
[18]
T. Nitta, A solution to the 4-bit parity problem with a single quaternary neuron, Neural Inf Process Lett Rev 5(2) (2004), 33–39.
[19]
T. Isokawa, T. Kusakabe, N. Matsui and F. Peper, Quaternion neural network and its application, LNAI 2774 (2003), 318–324.
[20]
D.B. Foggel, An information criterion for optimal neural network selection, IEEE Trans Neural Netw 2(5) (1991), 490–497.
[21]
E.N. Lorenz, Deterministic nonperiodic flow, Journal of the Atmospheric Sciences 20(2) (1963), 130–141.
[22]
L.O. Chua, T. Matsumoto and M. Komuro, The double scroll, IEEE Transactions on Circuits and Systems CAS 32(8) (1985), 798–818.
[23]
J. Xu and D.E. Root, Advances in artificial neural network models of active devices, 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Ottawa, ON, Canada, 2015.
[24]
X.G. Chen, Research on reliability of complex network for estimating network reliability, Journal of Intelligent & Fuzzy Systems 32(5) (2017), 3551–3560.
[25]
J. Zhai, T. Li and X. Wang, A cross-selection instance algorithm, Journal of Intelligent & Fuzzy Systems 30(2) (2016), 717–728.
[26]
M.I. Jordan and T.M. Mitchell, Machine learning: Trends, perspectives, and prospects, Science 349(6245) (2015), 255–260.
[27]
J. Zhai, X. Wang and X. Pang, Voting-based instance selection from large data sets with mapreduce and random weight networks, Information Sciences 367-368 (2016), 1066–1077.
[28]
S. Scardapane, S. Van Vaerenbergh, A. Hussain and A. Uncini, Complex-valued neural networks with nonparametric activation functions, IEEE Transactions on Emerging Topics in Computational Intelligence (2018), 1–11.
Index Terms
- On the learning machine with quaternionic domain neural network and its high-dimensional applications
Index terms have been assigned to the content through auto-classification.
Recommendations
On the learning machine in quaternionic domain and its application
There are various high-dimensional engineering and scientific applications in communication, control, robotics, computer vision, biometrics, etc.; where researchers are facing problem to design an intelligent and robust neural system which can process ...
Quaternionic Hopfield neural networks with twin-multistate activation function
In the present work, a Hopfield neural network with a new quaternionic activation function, referred to as a twin-multistate activation function, is proposed. The multistate activation function has been used in complex-valued Hopfield neural networks (...
Fixed points of split quaternionic hopfield neural networks
In a complex-valued phasor Hopfield neural network with a training pattern, only the rotated patterns are fixed points, while in a complex-valued K-state Hopfield neural network, there exist K fixed points. In the case of a quaternionic Hopfield neural ...
Comments
Information & Contributors
Information
Published In
© 2019 – IOS Press and the authors. All rights reserved.
Publisher
IOS Press
Netherlands
Publication History
Published: 01 January 2019
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 04 Sep 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in