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therefore later named as C XOR problem. It has been used to test the learning and
classification ability of real and complex domain neuron (with sigmoidal function)
through corresponding learning algorithms. The C XOR problem is one of the best
nonlinearly separable pattern associator in complex domain like popular XOR prob-
lem in real domain. The pattern set in C XOR is defined by following rules:
the real part of output is 1 if first input is equal to second input, otherwise it is 0.
the imaginary part of output is 1 if second input is either 1 or j, else it is 0.
This test problem is chosen with an eye toward testing the ability of the real and
complex domain neuron. The comparative learning speed is presented in Fig. 3.1 and
some of the observations on the key issues of optimization are given in Table 3.1 .
The neural network based on complex domain neuron is comparatively faster than
real domain neuron while the space complexity (number of learning parameters:
synaptic weights and bias) is only half whereas the time complexity (number of
computations per learning cycle: addition, subtraction, division, and multiplication)
remained almost same.
Fig. 3.1 Average learning speed of a sigmoidal neuron in real and complex domain for CXOR
problem
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