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A metric for quantifying nonlinearity in k -dimensional complex-valued functions

Document Type

Article

Publication Date

3-3-2022

Abstract

Modeling and simulation is a proven cost-efficient means for studying the behavioral dynamics of modern systems of systems. Our research is focused on evaluating the ability of neural networks to approximate multivariate, nonlinear, complex-valued functions. In order to evaluate the accuracy and performance of neural network approximations as a function of nonlinearity (NL), it is required to quantify the amount of NL present in the complex-valued function. In this paper, we introduce a metric for quantifying NL in multi-dimensional complex-valued functions. The metric is an extension of a real-valued NL metric into the k-dimensional complex domain. The metric is flexible as it uses discrete input–output data pairs instead of requiring closed-form continuous representations for calculating the NL of a function. The metric is calculated by generating a best-fit, least-squares solution (LSS) linear k-dimensional hyperplane for the function; calculating the L2 norm of the difference between the hyperplane and the function being evaluated; and scaling the result to yield a value between zero and one. The metric is easy to understand, generalizable to multiple dimensions, and has the added benefit that it does not require a closed-form continuous representation of the function being evaluated.

Comments

This article was published by Sage as an article of The Journal of Defense Modeling and Simulation (JDMS) ahead of inclusion in a published issue (as cited on this page). It is available to subscribers through the DOI link below.

Issue date: January 2024.

Source Publication

The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology

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