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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 (variables) 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).
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
starting to develop the software model.
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