288 pp. per issue
6 x 9, illustrated
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Neural Computation

May 2015, Vol. 27, No. 5, Pages 1120-1141
(doi: 10.1162/NECO_a_00729)
© 2015 Massachusetts Institute of Technology
Learning Dynamics of a Single Polar Variable Complex-Valued Neuron
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This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used.