Energy Discriminant Analysis, Quantum Logic, and Fuzzy sets

TL;DR

This paper introduces a novel approach to signal recognition using quantum logic and fuzzy sets, linking energy distributions to quantum density matrices for improved classification.

Contribution

It proposes using quantum logic of linear subspaces and fuzzy set interpretation for Bayesian energy discriminant classifiers, connecting quantum theory with pattern recognition.

Findings

Quantum logic can be applied to signal recognition.

Correlation matrices correspond to von Neumann density matrices.

Discriminant functions are interpreted as fuzzy set membership functions.

Abstract

In the paper, we show that quantum logic of linear subspaces can be used for recognition of random signals by a Bayesian energy discriminant classifier. The energy distribution on linear subspaces is described by the correlation matrix of the probability distribution. We show that the correlation matrix corresponds to von Neumann density matrix in quantum theory. We suggest the interpretation of quantum logic as a fuzzy logic of fuzzy sets. The use of quantum logic for recognition is based on the fact that the probability distribution of each class lies approximately in a lower-dimensional subspace of feature space. We offer the interpretation of discriminant functions as membership functions of fuzzy sets. Also we offer the quality functional for optimal choice of discriminant functions for recognition from some class of discriminant functions.