Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 97

Table 4.2 Comparison of training and testing performance for Ionosphere Data problem
S. No.

Training Neuron Network Average MSE Testing

algorithm type epochs training error (%)

R MLP 34-3-1 8,000 0.0068 6.7

1 R BP R RPN ( d = 0 . 85 ) 34-3-1 8,000 0.0092 6.0

R RSS 34-1-1 14,000 0.0095 7.3

R RSP 34-1-1 14,000 0.0090 6.0

R MLP 34-3-1 2,000 0.0094 7.3

2 R RPROP R RPN ( d = 0 . 85 ) 34-3-1 2,000 0.0083 6.0

R RSS 34-1-1 3,000 0.013 8.4

R RSP 34-1-1 3,000 0.012 8.0

C MLP 34-2-1 7,000 0.0065 6.0

3 C BP C RPN ( d = 0 . 85 ) 34-1-1 7,000 0.0070 4.0

C RSS 34-1 14,000 0.016 7.3

C RSP 34-1 14,000 0.0095 6.0

C MLP 34-2-1 1,500 0.001 6.0

C RPN ( d = 0 . 85 )

4 C RPROP 34-1-1 1,500 0.007 4.0

C RSS 34-1 3,000 0.013 8.0

C RSP 34-1 3,000 0.013 7.3

can approximate above four vector operations through a single network. Let z 1 =

r 1 e j ˑ 1 and z 2 r 2 e j ˑ 2 , where

5. Aset of 200
patterns was randomly chosen for training and approximation of trained network was
tested on other 1000 patterns. Table 4.3 analyzes the performance of different neuron-
based networks with two training algorithms viz C BP (

= − pi ≤ ˑ 1 ,ˑ 2 ≤ pi and 0 . 1 ≤ r ≤ 0 .

ʷ = 0 . 0005) and C RPROP

μ − = ,μ + = 10 ( − 6 ) ,ʔ max =

( 005) on above test

data. Results reported in Table 4.3 are from reasonably smaller network topology
which can yield fairly good accuracy. On increasing the number of neurons in a
hidden layer, performance measure in SUMand SUB operations are unaffected while
slow improvement is observed in MULT and QUOT operations. C RSP neuron-based
network outperforms, especially in approximation of MULT and QUOT operations
with quiet lesser number of learning parameters.

0 . 5 1 . 2 ,ʔ min = 0 . 001 ,ʔ 0 = 0 .

4.4.2.2 2D Gabor Function

The 2D Gabor function is a unique function that achieve the lower bound for the
space-frequency uncertainty product. It is a measure of a function's simultaneous
localization in both spatial and frequency domains. It is well known that the highly
oriented simple cell receptive fields in the visual cortex of mammals can be closely
modeled by 2D Gabor functions [ 46 ], which are Gaussians modulated by sinusoidal