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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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