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20     CHAPTER 1 Nature’s Learning Rule: The Hebbian-LMS Algorithm














































                         FIGURE 1.14
                         Histogram of responses of a selected neuron in the output layer of a three-layer Hebbian-
                         LMS network. (A) Before training (B) after training.


                         half-sigmoid output appears to be almost binary but it is not so. Observing the colors,
                         one can see that some of the clusters were split apart. After training, the histogram of
                         the half-sigmoid output shows the clusters to be intact and all together.



                         7. OTHER CLUSTERING ALGORITHMS
                         7.1 K-MEANS CLUSTERING

                         The K-means clustering algorithm [14,15] is one of the most simple and basic clus-
                         tering algorithms and has many variations. It is an algorithm to find K centroids and
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