MATLAB Code Implementation for Correlation Dimension Calculation

Our correlation dimension calculation program implements a complete workflow through three core computational stages. First, the correlation dimension calculation determines the local dimensionality of datasets using the Grassberger-Procaccia algorithm, which involves analyzing the scaling behavior of correlation sums. The implementation includes distance matrix computation and logarithmic regression analysis to extract the dimension estimate from the slope of the correlation integral curve. Second, we perform phase space reconstruction using Takens' embedding theorem, which maps high-dimensional data into lower-dimensional spaces through time-delay embedding. The code automatically optimizes embedding parameters (time delay and embedding dimension) using mutual information and false nearest neighbor methods, making complex data more tractable for analysis. Finally, the correlation integral calculation maps datasets into transformed spaces using pairwise distance analysis. This stage computes the probability that two points are within a specified distance epsilon, implemented through efficient vectorized operations for handling large datasets. The resulting integral provides fundamental insights for deeper data analysis, particularly in nonlinear time series analysis and chaos theory applications.