Complex-Valued Neural Network in Signal Processing: A Study on the Effectiveness of Complex Valued Generalized Mean Neuron Model
A complex valued neural network is a neural network
which consists of complex valued input and/or weights and/or thresholds
and/or activation functions. Complex-valued neural networks
have been widening the scope of applications not only in electronics
and informatics, but also in social systems. One of the most important
applications of the complex valued neural network is in signal
processing. In Neural networks, generalized mean neuron model
(GMN) is often discussed and studied. The GMN includes a new
aggregation function based on the concept of generalized mean of all
the inputs to the neuron. This paper aims to present exhaustive results
of using Generalized Mean Neuron model in a complex-valued neural
network model that uses the back-propagation algorithm (called
-Complex-BP-) for learning. Our experiments results demonstrate the
effectiveness of a Generalized Mean Neuron Model in a complex
plane for signal processing over a real valued neural network. We
have studied and stated various observations like effect of learning
rates, ranges of the initial weights randomly selected, error functions
used and number of iterations for the convergence of error required on
a Generalized Mean neural network model. Some inherent properties
of this complex back propagation algorithm are also studied and
discussed.
[1] A. Piegat, Fuzzy Modeling and Control, Physica-Verlag, Heidelberg, New
York, 2001.
[2] M.H.Housan, Fundamental of Artificial NEURAL network, Princeton
Hall Of India, 1998.
[3] Nitta T., "An Analysis of the Fundamental Structure of Complex-valued
Neurons", Neural Processing Letters, Vol.12, No.3, pp.239-246
[4] Nitta T., "Redundancy of the Parameters of the Complex-valued Neural
Networks", Neurocomputing, Vol.49, Issue 1-4, pp.423-428 (2002).
[5] Nitta T., "Solving the XOR Problem and the Detection of Symmetry
Using a Single Complex-valued Neuron", Neural Networks, Vol.16, No.8,
pp.1101-1105 (2003)
[6] Nitta T., "An Extension of the Back-Propagation Algorithm to Complex
Numbers", Neural Networks, Vol.10, No.8, pp.1391-1415 (1997)
[7] P. J. Werbos, Back propagation through time: what it does and how to
do it Proc. Of the IEEE 78(10):1550-1560, 1990.
[8] R.N. Yadav, P.K. Kalra and J. John, Neural network learning with
generalized mean based neuron model,, Springer Verlag
[9] http://www.blondertongue.com/QAM-Transmodulator/QAM defined.php
[10] http://www.psych.utoronto.ca/users/reingold/courses/ai/cache/InvSlides.html
[11] http://www.lycos.com/info/quadrature-amplitude-modulation.html
[1] A. Piegat, Fuzzy Modeling and Control, Physica-Verlag, Heidelberg, New
York, 2001.
[2] M.H.Housan, Fundamental of Artificial NEURAL network, Princeton
Hall Of India, 1998.
[3] Nitta T., "An Analysis of the Fundamental Structure of Complex-valued
Neurons", Neural Processing Letters, Vol.12, No.3, pp.239-246
[4] Nitta T., "Redundancy of the Parameters of the Complex-valued Neural
Networks", Neurocomputing, Vol.49, Issue 1-4, pp.423-428 (2002).
[5] Nitta T., "Solving the XOR Problem and the Detection of Symmetry
Using a Single Complex-valued Neuron", Neural Networks, Vol.16, No.8,
pp.1101-1105 (2003)
[6] Nitta T., "An Extension of the Back-Propagation Algorithm to Complex
Numbers", Neural Networks, Vol.10, No.8, pp.1391-1415 (1997)
[7] P. J. Werbos, Back propagation through time: what it does and how to
do it Proc. Of the IEEE 78(10):1550-1560, 1990.
[8] R.N. Yadav, P.K. Kalra and J. John, Neural network learning with
generalized mean based neuron model,, Springer Verlag
[9] http://www.blondertongue.com/QAM-Transmodulator/QAM defined.php
[10] http://www.psych.utoronto.ca/users/reingold/courses/ai/cache/InvSlides.html
[11] http://www.lycos.com/info/quadrature-amplitude-modulation.html
@article{"International Journal of Electrical, Electronic and Communication Sciences:52229", author = "Anupama Pande and Ashok Kumar Thakur and Swapnoneel Roy", title = "Complex-Valued Neural Network in Signal Processing: A Study on the Effectiveness of Complex Valued Generalized Mean Neuron Model", abstract = "A complex valued neural network is a neural network
which consists of complex valued input and/or weights and/or thresholds
and/or activation functions. Complex-valued neural networks
have been widening the scope of applications not only in electronics
and informatics, but also in social systems. One of the most important
applications of the complex valued neural network is in signal
processing. In Neural networks, generalized mean neuron model
(GMN) is often discussed and studied. The GMN includes a new
aggregation function based on the concept of generalized mean of all
the inputs to the neuron. This paper aims to present exhaustive results
of using Generalized Mean Neuron model in a complex-valued neural
network model that uses the back-propagation algorithm (called
-Complex-BP-) for learning. Our experiments results demonstrate the
effectiveness of a Generalized Mean Neuron Model in a complex
plane for signal processing over a real valued neural network. We
have studied and stated various observations like effect of learning
rates, ranges of the initial weights randomly selected, error functions
used and number of iterations for the convergence of error required on
a Generalized Mean neural network model. Some inherent properties
of this complex back propagation algorithm are also studied and
discussed.", keywords = "Complex valued neural network, Generalized Meanneuron model, Signal processing.", volume = "2", number = "1", pages = "37-6", }