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C++ API

Function File: [dim, frac, avgsize, avgsrtsize] = false_nearest (S)
Function File: … = false_nearest (S, paramName, paramValue, …)

Determines the fraction of false nearest neighbors.

Input

S

This function always assumes that each time series is along the longer dimension of matrix S. It also assumes that every dimension (counting along the shorter dimension) of S is considered a component of the time series. So 

S = [[1:1000];[5:1004]]

would be considered a 2 component, 1000 element time series.

Parameters

minemb

This is the flag ’-m’ from TISEAN. It is the minimal embedding dimensions of the vectors [default = 1].

maxemb

This parameter is consistent with the second part of the flag ’-M’ from TISEAN. The first part of that flag is unnecessary as this function assumes that all components of the input data are used. This parameter determines the maximum embedding dimension of the vectors [default = 5].

d

The delay of the vectors [default = 1].

t

The theiler window [default = 0].

f

Ratio factor [default = 2.0].

Switches

verbose

If this switch is selected the function will give progress reports along the way.

Outputs

dim

This holds the dimension of the output data.

frac

The fraction of false nearest neighbors.

avgsize

The average size of the neighborhood.

avgrtsize

The average of the squared size of the neighborhood.

See also: http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/docs_c/false_nearest.html or demo for more information.

Algorithms

The algorithms for this functions have been taken from the TISEAN package.

Demonstration 1

The following code

 ikd          = ikeda (10000);
 hen          = henon (10000);
 hen_noise    = hen + mean (hen) * 0.01 .* (-6 + sum (rand ([size(hen), 12]), 3));
 [dikd, fikd] = false_nearest (ikd(:,1));
 [dhen, fhen] = false_nearest (hen(:,1));
 [dhno, fhno] = false_nearest (hen_noise(:,1));
 plot (dikd, fikd, '-b*', 'markersize', 15,...
       dhen, fhen, '-r+', 'markersize', 15,...
       dhno, fhno, '-gx', 'markersize', 15);
 legend ("Ikeda", "Henon", "Noisy Henon");
 ylim ([0, 1]);

Produces the following figure

Figure 1

Package: tisean