New types of nonlinear auto-correlations of bivariate data and their applications

TL;DR

This paper develops new nonlinear auto-correlation methods for bivariate data, enabling better signal matching and attractor reconstruction, with applications demonstrated through attractor analysis and a novel ellipsoid fitting technique.

Contribution

It introduces new types of nonlinear auto-correlations and a novel attractor quantification method called ellipsoid fit for bivariate data analysis.

Findings

New nonlinear auto-correlation types effectively match signals with different nonlinearities.

Reconstructed three-dimensional attractors using derived coordinates.

Ellipsoid fit provides a quantitative measure of attractor differences.

Abstract

The paper introduces new types of nonlinear correlations between bivariate data sets and derives nonlinear auto-correlations on the same data set. These auto-correlations are of different types to match signals with different types of nonlinearities. Examples are cited in all cases to make the definitions meaningful. Next correlogram diagrams are drawn separately in all cases; from these diagrams proper time lags/delays are determined. These give rise to independent coordinates of the attractors. Finally three dimensional attractors are reconstructed in each case separately with the help of these independent coordinates. Moreover for the purpose of making proper distinction between the signals, the attractors so reconstructed are quantified by a new technique called ellipsoid fit.