False Nearest Neighbors dialog box

 

Use this dialog box to compute the percentage of nearest neighbors that are lost in going from a n- dimensional embedding to a n+1 dimensions in selected series.  The statistic is computed as a function from a minimum embedding for a number of steps.  The false nearest neighbors algorithm is used to determine a minimal embedding dimension.  This dimension is taken to be the first at which no nearest neighbors are lost in going from that embedding to the next because at this point the attractor is considered to be unfolded in state space.

 

Refer to Kennel, Brown and Abarbanel (1992), Abarbanel (1995) and Kennel and Abarbanel (2002) for additional information on this subject.

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid extents in the Input Range box.

 

Input Range

Type in this box the range of cells you want to use as input for this command.

 

Series in Rows

Check this box to indicate that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Series Context

 

Single Series

Select this option to specify that the data specified by the Input Range box represent individual series.

 

Multivariate

Select this option to specify that the data specified by the Input Range box represent one multidimensional series.

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Plot

Check this box to plot the results of this operation.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Options

 

Min. Embedding

Type in this box the minimum dimensional embedding at which to begin calculating nearest neighbors.

 

Embedding Steps

Type in this box the number of embedding steps for which you want to calculate the percentage of nearest neighbors. For example, if you typed 3 in Min. Embedding and 5 in Embedding Steps, the percentage of nearest neighbors will be calculated for 3, 4, 5, 6 and 7 dimensions.

 

Time Delay

Specifies the time delay that will be used to embed the selected series.  Type in this box the delay that will be used between the dimensional components of the embedding.

 

Refer to the Average Mutual Information dialog box for additional information on time delays.

 

Exclusion Window

Type in this box an integer number to exclude nearest neighbors in the temporal vicinity of points.  For example, typing 10 in this box would exclude all nearest neighbors that are within 10 time steps away from the reference points.

 

Local Tolerance

Specifies the local tolerance for considering nearest neighbors. Typical values for this parameter are between 10 and 20.

 

Global Tolerance

Specifies the global tolerance for considering nearest neighbors in accordance to Kennel and Abarbanel (2002).  Typical values for this parameter are between 1 and 2.

 

 

Reference Points

This is the fraction of points that will be used in calculating this operation.  To avoid using the complete series, type in this box a floating point number larger than zero and equal or smaller than one. A number lower than one will force the algorithm to limit the number of points to that fraction from the input series.  Selected points are re-sampled at equal intervals from the original series.  This option is particularly useful if the precision of the operation is not critical (an approximation suffices) and the length of the input series is large.

 

 

Choose at Random

Check this box if you want the reference points to be chosen at random, instead of re-sampled at equal intervals from the original series.

 

Distance Metric

Specifies the method by which distances are computed.

 

Loo - Max

Select this option if you want to use the Minkowski Max, , distance metric for measuring neighborhood distances.

 

L1 - Manhattan

Select this option if you want to use the Minkowski Manhattan, L1, distance metric for measuring neighborhood distances.

 

L2 - Euclidean

Select this option if you want to use the Minkowski Euclidean, L2, distance metric for measuring neighborhood distances.

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.