This paper is concerned with the solution of the principal component analysis (PCA) problem with the aid of neural networks (NNs). After an overview of the basic NN-based PCA concepts and a listing of the available algorithms, two criteria for evaluating PCA NN algorithms are proposed. Then, a new criterion for the generation of improved PCA NN structures with reduced size is presented. Using this criterion, one can start with a small network and dynamically add new nodes at the hidden layer(s) during training, one at a time, until the desired performance is achieved. A simulation example is provided that shows the applicability and effectiveness of the methodology.