Hopfield Network Associative Memory Lab Report

ABSTRACT- This paper presents the implementation of a Hebbian learning rule and genetic algorithm to store and later, recall of superimposed images of numerals in Hopfield network associative memory. A set of ten objects (i.e. 0 to 9 numerals) has been considered as the pattern set. In the Hopfield network associative memory, the weighted code of input patterns provides an auto-associative function in the network. The storing of images is done by hebbian learning rule and recalling is done by using both hebbian rule and genetic algorithm. The simulated results shows that the genetic algorithm gives efficient results as compared to hebbian rule for superimposed images of numerals. Keywords- Hopfield Neural network, associative memory, hebbian
(7,1) 0.4 0.2 99.4 0.6 39.0 26.7 34.3 65.7
(7,2) 0.4 0.9 98.7 1.3 32.5 63.3 4.2 95.8
(7,3) 0.1 0.6 99.3 0.7 29.3 10.6 60.1 39.9
(7,4) 0.8 0.8 98.4 1.6 42.3 41.3 16.4 83.6
(7,5) 0.4 0.8 98.8 1.2 22.7 35.6 41.7 58.3
(7,6) 0.1 1 98.9 1.1 19.6 56.9 23.5 76.5
(7,8) 0 0.4 99.6 0.4 5.9 35.6 58.5 41.5
(7,9) 0.8 0.5 98.7 1.3 45.9 22.9 31.2 68.8

Graph 8: Results when 7 superimposed with other numerals (0 to 9)

Table 11: Results when 8 superimposed with other numerals (0 to 9) After 1000 iterations success (%) By Hebb's rule By Genetic algorithm
Numerals mixed together Numerals identified as '8' Numerals identified as the other numerals from super-imposed images Numerals not identified Total success Numerals identified as '8' Numerals identified as the other numerals from super-imposed images Numerals not identified Total success
(8,0) 1 0.8 98.2 1.8 35.6 32.6 31.8 68.2
(8,1) 1.3 0.4 98.3 1.7 15.3 38.6 46.1 53.9
(8,2) 0.2 0 99.8 0.2 19.2 9.3 71.5 28.5
(8,3) 0.3 0.6 99.1 0.9 31.8 25.6 42.6 57.4
(8,4) 0 1 99 1 12.0 45.9 42.1 57.9
(8,5) 0.9 0.4 98.7 1.3 54.6 21.9 23.5 76.5
(8,6) 0 100 0 100 6.9 93.1 0 100
(8,7) 0 0.4 99.6 0.4 5.9 35.6 58.5 41.5
(8,9) 100 0 0 100 100 0 0 100

Graph 9: Results when 8 superimposed with other numerals (0 to