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Summary: LETTER Communicated by Simon Haykin
Approximation by Fully Complex Multilayer Perceptrons
Taehwan Kim
tkim@mitre.org
MITRE Corporation, McLean, Virginia 22102 U.S.A.
T šulay Adalõ
adali@umbc.edu
Department of Computer Science and Electrical Engineering, University of Maryland
Baltimore County, Baltimore, Maryland 21250 U.S.A.
Weinvestigate theapproximation ability of amultilayer perceptron (MLP)
network when it is extended to the complex domain. The main challenge
for processing complex data with neural networks has been the lack of
bounded and analytic complex nonlinear activation functions in the com-
plex domain, as stated by Liouville's theorem. To avoid the con ict be-
tween the boundedness and the analyticity of a nonlinear complex func-
tion in the complex domain, a number of ad hoc MLPs that include using
two real-valued MLPs, one processing the real part and the other pro-
cessing the imaginary part, have been traditionally employed. However,
since nonanalytic functions do not meet the Cauchy-Riemann conditions,
they render themselves into degenerative backpropagation algorithms
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