As expected, the results show that lower frequency separation requires more samples and/or iterations to train. Also, even if training is successful, proper classification of the noisy signals gets very difficult for smaller frequency separations. For frequency separations of 100% and 10%, training was successful after 100 epochs using 64 samples per cycle. As shown in Figures 6(a) and 6(b) proper classification was made for 100% separation with a signal to noise ratio of 1, and for 10% separation with a signal to noise ratio of 10.
Figure 6(c) shows that for a separation of 5% it was necessary to increase the number of epochs to 500 to train the network, but proper classification of only 2 of the 3 signals was made at a signal to noise ratio of 10. Finally Figure 6(d) shows that successful learning required many more samples per cycle (1000) as well as epochs (10000), but one of the 3 signals was still not classified even for a signal to noise ratio as high as 100. As was the case in the previous example, results are not necessarily repeatable due to the randomness of the noise.
III. Unsupervised Learning
A. Introduction to Kohonen Self-Organizing Maps
The Kohonen algorithm is applied to unsupervised learning, where target values are not specified. The associated Self Organizing Map (SOM) is a topological structure made up of cluster units. The training algorithm also builds in "competition" among neurons. Learning is restricted to neurons that are either "winners" (or are neighboring units to "winners") of a competition relating to the closeness of weights to inputs. The SOM uses the competition among neurons to learn, in an unsupervised way, how to group input data into clusters. A cluster unit is somewhat analogous to an output corresponding to a group of input patterns, in a supervised learning situation. Interestingly, cluster units are a property observed in the brain.
Cluster units can be organized in either a one-dimensional or two-dimensional fashion. The one-dimensional unit is called a linear array whereas a two-dimensional unit can be arranged as either a rectangular or hexagonal grid. Illustrations of a part of a linear array and a rectangular grid are shown below. The "winning unit" of a particular competition is designated by "#" and neighboring units within a "radius" R are shown as "*".