Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 95

4.4 Performance Variation Among Conventional
and Higher-Order Neurons

In order to estimate the strength and effectiveness of a neural network of consid-
ered higher-order neurons with learning algorithms in real and complex domain, this
section presents performance evaluation on different types of problems in real and
complex domain. In case of real-valued problems, the input-output data is assigned
to real part and the value very close to zero is assigned to imaginary part, to get the
complex-valued data [ 25 , 34 ]. The results obtained are comparedwith the ones shown
by other neural networks and training algorithms. An intelligent choice of RPROP
parameters and weight initialization gives good results. The computational power
and approximation capability have been compared in terms of number of epochs,
learning parameters, network topology, and testing error along with other statistical
performance evaluation metrics like correlation, error variance, and Akaikes infor-
mation criteria (AIC) [ 44 ]. AIC evaluates the goodness of fit of model based on mean
square error for training data and number of estimated parameters. For analysis pur-
poses, the number of learning parameters in each complex-valued weight is counted
as two [ 32 ].

4.4.1 Real Domain Problems

4.4.1.1 The Wine Recognition Data Problem

The wine dataset is a result of chemical analysis of wine with 13 constituents found
in each of the three types of wines. Dataset in [ 45 ] provide 178 instances of all three
classes. In our experiments some random 60% data are taken for training and rest
40% for testing. The performance result using different type of networks with four
training algorithms viz R BP , C BP (with

ʷ = 0 . 003) and R RPROP , C RPROP (with

μ − ,μ + 10 ( − 6 ) ,ʔ max 1) is presented in

Table 4.1 . A very poor convergence is observed with backpropagation algorithm. The
number of training epochs is drastically reduced when proposed C RPROP algorithm
is used for training. The significant advantage of using C RPROP algorithm is that
a perfect result (no misclassification) is achieved with least training epochs. Results
reveals the superiority of the different neurons in a complex domain in all respects.

= 0 . 5 = 1 . 2 ,ʔ min = = 0 . 005 ,ʔ 0 = 0 .

4.4.1.2 Ionosphere Data

This radar data was collected by a system in Goose Bay, Labrador, Johns Hopkins
University and available in the database [ 45 ]. These radar returns belongs to two
classes, “Good” radar returns are those showing evidence of some type of structure
in the ionosphere and “Bad” returns are those that do not, their signals pass through