Principal component analysis using self-organized neural network

The method principal component (PCA) allows to allocate from a matrix of these several objects with a large amount of signs only 1-3 vectors containing 90-95% of information. Usually measuring problem of assessment of these main components is solved by the iterative NIPALS procedure or the algebraic SVD procedure, however both of these methods often give ambiguous estimates. For the purpose of elimination of ambiguity, alternative approach to measurement main component on the basis of the self-adjusted neural network is offered. Convergence analysis shows that the single neuron governed by the self-organized learning rule, adaptively extracts the first principal component of the input signal. Considered two options of the stabilization of Hebbian algorithm: a) with the weight normalization dividing by Euclid's RMS according to the equation; b) with the weight cancellation according to the equation. Parameters of the speed adjustment vary considerably for these algorithms, however, the summary values of weights compare within the four decimal digits.