    Next: Problems with a Small Up: Experimental Evaluation Previous: Test Methodology

Binary Pattern Recognition Figure 7.1:  The Four Original Pictures. Figure 7.2:  Examples of Distorted Pictures.

For problems in pattern recognition, particularly for binary patterns, logical neural networks have been proved to be very useful. LNN can perform a classification according to the distance between the test and training patterns. The hypothesis is that a modular neural network should outperform a monolithic network on this domain; because the internal structure of a MNN is similar to a LNN.

In this experiment different networks were trained to memorize four different but similar binary pictures, shown in Figure 7.1. The pictures had a size of 66 by 83 pixels (5478 binary input variables).

After the networks had successfully learnt the training set, a number of distorted pictures were presented. Examples of the distorted pictures are given in Figure 7.2, and the full picture set is given in appendix C. The task was to assign the class number to each picture.

As expected the RAM based logical network performed very well on this problem. For a RAM size of 256 (eight inputs) a recognition performance of 100% was achieved. This good result was achieved because the number of instances in the training set was very small.

Twelve modular networks using between 548 and three input modules were tested. The mapping function $π$ was a random permutation. The number of training steps in the input layer and in the decision network was varied. Different learning parameters and momentum values were used. Throughout the experiment the modular network converged for nearly any setting of the parameters.

Four different monolithic networks were trained; they had different numbers of hidden layers and different numbers of neurons. It was difficult to find a parameter set that ensured convergence for the training. In Table 7.1 some of the best results gained with these networks are presented.

 Network $P$G Time $M$1=(5478,4,[32,16,8]) 72.0% 12' $M$2=(5478,4,[8,6]) 77.7% 3'26'' $N$1=(5478,4,548,small,π,(10,2,),(1096,4,)) 88.8% 2'28'' $N$2=(5478,4,110,small,π,(50,2,),(220,4,)) 91.6% 1'36'' $N$3=(5478,4,28,small,π,(200,2,),(56,4,)) 86.1% 4'32''

The maximum performance of the modular network was significantly better than the best result achieved with a monolithic network, but did not achieve the perfect recognition of the logical network. Figure 7.3:  Comparison of the Best Networks for the Binary Recognition Task.

In Figure 7.3 a comparison of the best networks of each type is given. It can be seen that the LNN is the most suitable for this application domain (small number of binary patterns, high dimensional input space). It delivered the best generalization performance with the shortest training time.    Next: Problems with a Small Up: Experimental Evaluation Previous: Test Methodology

Albrecht Schmidt
Mit Okt 4 16:45:34 CEST 2000