Estimate the acceptable minimum embedding dimension

Estimate the acceptable minimum embedding dimension.

`est_dimension_w_fnn`

dev

Estimate the acceptable minimum embedding dimension using False Nearest Neighbors Algorithm [Kennel_1992].

Select $xk$ appropriately from the embedded data with dimension $d$ , find the closest tangent vector $xn$ , and set the distance to $Rkn$ . It is embedded from 1 to D_max. Calculate the closest distance for all data. The points that satisfy the following two conditions are counted. $Atol$ (threshold_A) and $Rtol$ (threshold_R) are thresholds.

$\Biggl( \frac{R_{d+1}^2(k, n)-R_d^2(k, n)}{R_d^2(k, n)} \Biggr)^\frac{1}{2}>R_{tol}$

$\frac{R_{d+1}(k, n)}{R_A}>A_{tol}$

$RA$ is the standard deviation obtained from the time series.
Let the acceptable minimum embedding dimension be the first dimension below 1% (threshold_percent) in the percentages obtained for each embedded dimension.

By default, the actual calculation result is displayed. The point actually adopted is red. If you want to turn off the display, give plot=False.

from hundun.exploration import est_dimension_w_fnn

Parameters

u_seq
T
D_max=10
threshold_R=10
threshold_A=2
threshold_percent=1
plot=True
path_save_plot=None

Returns

dimension
percentages: numpy.ndarray

Example

Estimate the acceptable minimum embedding dimension for x in the Lorenz time series.

from hundun.equations import Lorenz
from hundun.exploration import est_dimension_w_fnn


x_seq = Lorenz.get_u_seq(25000)[::5, 0]
D, percentages = est_dimension_w_fnn(x_seq, T=10)
print(D)