CRP Toolbox Reference

ace

Purpose

Finds optimal transformation and maximal correlation.

Syntax

    mcor=ace(x,y,[w,ii,oi])
    [theta, phi]=ace(x,y,[,w,ii,oi])
    [theta, phi, mcor]=ace(x,y,[,w,ii,oi])
    [theta, phi, mcor, i, o, imax, omax]=ace(x,y,[,w,ii,oi])

Description

Estimates the optimal transformations of the system theta(x)=phi(x) and computes the resulting maximal correlation mcor, where x is a one-column vector and y can be a multi-column vector.

[theta, phi, mcor, i, o, imax, omax]=ace(x,y [,w,ii,oi]) estimates the optimal transformations theta, phi and the maximal correlation mcor and outputs the number of inner iterations i, break-up number of inner inner iterations, number of outer iterations o and break-up number of outer inner iterations. If the algorithm doesn't converge, the number of iterations will be negative signed.

Without output arguments, ace plots the optimal transformations theta and phi.

Parameters

w is the half-length of the boxcar window, ii is the maximal number of inner iterations, oi is the minimal number of outer iterations.

Examples

    x=(-1:.002:1)+.3*rand(1,1001);
    y=(-1:.002:1).^2+.3*rand(1,1001);
    corrcoef(x,y)
    ace(y,x)

See Also

mcf

References

Breiman, L., Friedman, J. H.: Estimating Optimal Transformations for Multiple regression and Correlation, J. Am. Stat. Assoc., 80(391), 1985.

Voss, H., Kurths, J.: Reconstruction of nonlinear time delay models from data by the use of optimal transformations, Phys. Lett. A, 234, 1997.

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