2.2.6. False Nearest Neighbors (FNN) for dimension (n)

teaspoon.parameter_selection.FNN_n.FNN_n(ts, tau, maxDim=10, plotting=False, Rtol=15, Atol=2, Stol=0.9, threshold=10, method=None)

This function implements the False Nearest Neighbors (FNN) algorithm described by Kennel et al. to select the minimum embedding dimension.

Parameters:

• ts (array) – Time series (1d).

• tau (int) – Embedding delay.

Kwargs:

maxDim (int): maximum dimension in dimension search. Default is 10.

plotting (bool): Plotting for user interpretation. Default is False.

Rtol (float): Ratio tolerance. Default is 15. (10 recommended for false strands)

Atol (float): A tolerance. Default is 2.

Stol (float): S tolerance. Default is 0.9.

threshold (float): Tolerance threshold for percent of nearest neighbors. Default is 10%.

method (string): ‘strand’ Use the composite false nearest strands algorithm (David Chelidze 2017), ‘cao’ Use the Cao method (Cao 1996). Default is None.

Returns:

n, The embedding dimension.

Return type:

(int)

The following is an example implementing the False Nearest Neighbors (FNN) algorithm for the dimension:

from teaspoon.parameter_selection.FNN_n import FNN_n
import numpy as np

fs = 10
t = np.linspace(0, 100, fs*100)
ts = np.sin(t)

tau=15 #embedding delay

perc_FNN, n = FNN_n(ts, tau, plotting = True)
print('FNN embedding Dimension: ',n)

Where the output for this example is:

FNN embedding Dimension:  2