By Fyfe C.
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Additional resources for Artificial Neural Networks and Information Theory
1 Annealing of Learning Rate The mathematical theory of learning in Principal Component Nets requires the learning rate to be such that αk ≥ 0, α2k < ∞, αk = ∞. In practise, we relax these requirements somewhat and we find that we can generally find an approximation to the Principal Components when we use a small learning rate. However for more accurate results we can anneal the learning rate to zero during the course of the experiment. g. to subtract a small constant from the learning rate at each iteration, to multiply the learning rate by a number < 1 during the course of each iteration, to have a fixed learing rate for the first 1000 iterations and then to anneal it and so on.
12) 44 CHAPTER 3. 13) where the last term, O(α2 ) denotes terms which contain a term in the square or higher powers of α which we can ignore if α << 1. Therefore we can look at Oja’s rule as an approximation to the simple Hebbian learning followed by an explicit renormalisation. 5 Recent PCA Models We will consider 3 of the most popular PCA models. It is of interest to begin with the development of Oja’s models over recent years. 1 Oja’s Subspace Algorithm The One Neuron network reviewed in the last section is capable of finding only the first Principal Component.
All data is zero mean. Therefore, the largest eigenvalue of the input data’s covariance matrix comes from the first input, x1 , the second largest comes from x2 and so on. The advantage of using such data is that it is easy to identify the principal eigenvectors (and hence the principal subspace). There are 3 interneurons in the network and it can be seen that the 3-dimensional subspace corresponding to the first 3 principal components has been identified by the weights. e. in directions 4 and 5.
Artificial Neural Networks and Information Theory by Fyfe C.