By Fyfe C.
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Clearly the degree of accuracy of the convergence depends very greatly on the relative proportion of the amount of variance due to the length of the distribution from which points were drawn and the white noise. In the third case, the noise was of the same order as the variance due to the spread of points on the line and the convergence was severly disrupted. 8. 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 = ∞.
E. as information from the environment becomes available we use it for learning in the network. We are, however, really calculating the Principal Components of a sample, but since these estimators can be shown to be unbiased and to have variance which tends to zero as the number of samples increases, we are justified in equating the sample PCA with the PCA of the distribution. The adaptive/recursive methodology used in ANNs is particularly important if storage constraints are important. 2. Strictly, PCA is only defined for stationary distributions.
X = |wi ||x| cos θ where |d| is the length of d and θ is the angle between the 2 vectors. This is maximised when the angle between the vectors is 0. Thus, if w1 is the weight into the first neuron which converges to the first Principal Component, the first neuron will maximally transmit information along the direction of greatest correlation, the second along the next largest, etc. 3, we are equating with those of maximal information transfer through the system. Given that there are statistical packages which find Principal Components, we should ask why it is necessary to reinvent the wheel using Artificial Neural Networks.