The Non-Linear PCA Algorithm and Blind Source Separation
In this chapter, Oja’s non-linear PCA algorithm is considered in detail. The signal separating properties exhibited by the algorithm are also studied. The non-linear PCA learning rule is an approximate stochastic gradient descent algorithm to minimise the mean square error incurred in representing a vector by a nonlinear projection onto a basis of reduced dimensionality. By considering the original cost function from a differing perspective we can show that the algorithm is in fact, an approximate stochastic equivalent to the batch algorithm proposed and developed by Comon.