On the analysis of multidimensional linear predictive autoregressive data by a class of single layer connectionist models

A class of single layer connectionist models whose input consists of multivariable data which can be modelled by a multivariable linear predictive or autoregressive process is analysed. A solution is given for the linear and nonlinear cases, together with expressions relating to the network weight matrices and the linear predictive coefficient matrices. It is shown that the network performs a type of linear prediction where sums of data vectors can be modelled by linear combinations of sums of previous data vectors. This leads to an alternative simplified connectionist structure. Based on this a form of connectionist vector quantisation structure is suggested, for example for image classification, which is analogous to conventional structures. In addition, a link is made with the error back propagation algorithm. Also, it is shown that the results for a scalar autoregressive process generalise to a multivariable autoregressive process