Robust principal component extracting neural networks

We present a modification of Oja´s single unit PC learning rule that behaves optimally in a certain sense, if the unit output value - the representation value of the input signal - is corrupted with noise. The mathematical formulation of the problem falls under the name noisy principal component analysis (PCA) whose analytical solution for the single component case is presented here. Both Oja´s rule and the proposed robust PCA rule lead to zero solution as the noise power gets high, but the noise tolerance of the new rule is twice as large as Oja´s rule; in the noise-free case both rules behave identically