simpleCorrelationDi​mension

Simple and fast correlation dimension estimator.

Correlation dimension estimator of a set X of points that is extremely simple because it evaluates only the two nearest neighbors of the points within the set being examined.

The method has been introduced in:

Krakovská, A and Chvosteková, M. Simple correlation dimension estimator and its use to detect causality. Chaos, Solitons & Fractals 175 (2023): 113975

Description

D2 = simpleCorrelationDimension(X) estimates the correlation dimension of the set of points X.

X: The input data matrix (T x D), where T represents length of data and D is the dimension (number of vector coordinates)

D2: The output - estimation of the correlation dimension of X

The precision of the outcome increases as the input data more uniformly spans the analyzed dataset.

Example of use:

X = importdata('Lorenz.txt');

D2lorenz=simpleCorrelationDimension(X);

When dealing with one-dimensional data (time series), you can begin by utilizing the MATLAB function "phase SpaceReconstruction" to construct the matrix X. However, it is essential to validate the assumption that the data is an observation of a multivariate dynamical system, as stipulated by Takens' theorem.