A subspace approach to invariant pattern recognition using Hopfield networks

A pattern recognition system which uses a method of subspace projection to compare an n-point template and unknown patterns is considered. The system is intrinsically invariant to linear transformations, though dependent on the relative ordering of the points within the template and unknown. However, invariance to point ordering may be added through the use of a Hopfield network as an optimization tool. Finding the correct point ordering is formulated as a combinatorial optimization problem, and then mapped onto a modified Hopfield network for solution. The overall pattern recognition system is successfully used to recognize instances of the ten handwritten digits. The results confirm that the system is invariant to both linear transformations and point ordering