Neural Minor Component Analysis and TLS

Abstract

The TLS problem can be solved by using neural networks. However, this method can be better described in the framework of iterative numerical methods for TLS. This is justified by the separation between the neural and the numerical experts. The inexperience of the neural experts in numerical analysis also explains the confusion in the neural literature about the Minor Component Analysis (MCA) and the TLS. This paper shows the exact difference between MCA and TLS techniques and the algorithmic consequences. The MCA neural networks are presented, analysed and compared, above all for large sets of linear equations. The superiority of the MCA EXIN neural network is emphasized. In the end the TLS neural networks are described. The TLS EXIN neural network (derived from MCA EXIN) is the best technique and has very important properties, like the existence of universal initial conditions, the possibility to be accelerated and to solve the nongeneric TLS problem automatically.