Embedding Dimension Estimate with Confidence Limits

Estimate embedding dimension for a signal from a chaotic or non-chaotic system. This algorithm gives a confidence in the final result.

MATLAB function for estimating embedding dimension
based on T. L. Carroll and J. M. Byers, Chaos 27, 023101 (2017)

dimension function is
[probability_matrix] = embedding_prob_func(data_vector, delay_vector, dimension_vector,eigenvalue_table, surrogate)

Test script is dimension_function_test.m

Table of eigenvalues for a random matrix is eigenvalue_table.mat

Test signal from the Rossler system is rossler_train_signal.mat
ross_sig_train is 3 columns corresponding to rossler x,y and z variables
Choose one of the columns.

In the sample program, I use the first 5000 points from the x variable
I look at embedding dimensions of 2,3,4 and 5 and delays of 1 to 20

The output is a probability matrix. For each dimension and delay, the probability matrix indicates the probability that the Rossler system can be embedded in that many dimensions with that delay.

The variable surrogate is set to 0 or 1. If surrogate=1, then a surrogate for the data_vector is created by phase randomizing the signal. The probabilities from the surrogate are subtracted from the probabilities for the regular signal. The surrogate is used to make sure that that the data signal isn’t a filtered noise signal. If you know for sure that the data isn’t filtered noise, surrogate can be set to 0.