A class of simple nonlinear 1-unit PCA neural networks

This paper proposes a class of principal component analysis (PCA) neural networks that have a nonlinear input-output relationship and learn the first principal component in the input data. Each member of the class is characterized by a parameter p in the range (-1, 1) and trains its weight vector w by the learning rule: Δw=γ [x.sign(x^Tw) |x^Tw|^p-w], where γ is the gain factor and x is the input vector. The loss-term, -w, is much simpler than the typical feedback loss-terms of other 1-unit PCA neural networks in literature and still prevents the weight vector length from growing out of bound. The authors characterize solutions to which the neural networks converge mathematically, and confirm convergence to these solutions by simulation