tech report

[Mathew Yeates]

The following technical report (JPL Publication) is available
for anonymous ftp from the neuroprose directory at
cheops.cis.ohio-state.edu. This is a short version of a previous
paper "An Architecture With Neural Network Characteristics for Least
Squares Problems" and has appeared in various forms at several
conferences.

There are two ideas that may be of interest:
1) By making the input layer of a single layer Perceptron fully
   connected, the learning scheme approximates Newtons algorithm
   instead of steepest descent.
2) By allowing local interactions between synapses the network can
   handle time varying behavior. Specifically, the network can
   implement the Kalman Filter for estimating the state of a linear
   system.

get both yeates.pseudo-kalman.ps.Z and
         yeates.pseudo-kalman-fig.ps.Z

    A Neural Network for Computing the Pseudo-Inverse of a Matrix
            and Applications to Kalman Filtering

                     Mathew C. Yeates
            California Institute of Technology
                 Jet Propulsion Laboratory

ABSTRACT

A single layer linear neural network for associative memory is
described. The matrix which best maps a set of input keys to desired 
output targets is computed recursively by the network using a parallel
implementation of Greville's algorithm. This model differs from the 
Perceptron in that the input layer is fully interconnected leading
to a parallel approximation to Newtons algorithm. This is in contrast
to the steepest descent algorithm implemented by the Perceptron.
By further extending the model to allow synapse updates to interact
locally, a biologically plausible addition, the network implements
Kalman filtering for a single output system.