Another neural network that can perform PCA was proposed by Rubner and Tavan (in Rubner, J. and Tavan, P., A Self-Organizing Network for Principal-Components Analysis, Europhysics Letters, 10(7), 1989). Their approach, however, is based on the decorrelation of the covariance matrix, which is the final result of PCA (that is, it is like operating with a bottom-up strategy, while the standard procedure is top-down). Let's consider a zero-centered dataset, X, and a network whose output is y ∈ ℜm vectors. Therefore, the covariance matrix of the output distribution is as follows:
Structure of a generic Rubner-Tavan's network ...
