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One of the main problems of Pattern
Recognition is related to the Norm used to calculate vector distances. The
most used Norms are the Euclidean Distance (L2 Norm), the Manhattan
Distance (L1 Norm or Polyhedral Volume Influence Field) and the Box
Distance (LSUP Norm, L-Infinity Norm or Hyper-Cube Influence Field).
The L2 Norm and L1 Norm guarantee excellent
generalization and are typically preferred in pattern recognition applied
to images, but they can be deceived quite easily. The LSUP Norm is very
sensitive to noise on single vector components and hardly applicable to
images but it can be very difficult to deceive. The philosopher's stone of
Norm is the Perceptual Neighborhood.
We have been experimenting with
algorithms based on Perceptual Neighborhood and Modified Restricted Coulomb
Energy.
The goal of the new metric is the
maximization of the product Generalization * Robustness and the
minimization of the parameters.
A P3N™ (Perceptual Neighborhood
Neural Network™) is a neural network based on a Data-Base of humanly
indistinguishable Perceptual Influence Fields. We have currently defined
the mathematical model of the neural classifier P3N™ based on perceptual
neighborhoods and we are developing the software model.
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