Algorithms for Estimating Correlation Dimension

This text discusses three distinct algorithms for estimating correlation dimension: the G-P algorithm (corrint.m), Gaussian kernel association algorithm (gka.m), and Judd algorithm (judd.m). Each algorithm is built upon different mathematical models and theoretical foundations, featuring unique advantages, limitations, and application scopes. For instance, the G-P algorithm implemented in corrint.m calculates correlation integrals through pairwise point distance analysis, making it particularly suitable for data with linear correlations. Meanwhile, the Gaussian kernel association algorithm in gka.m employs smooth kernel functions to handle nonlinear correlations more effectively. The Judd algorithm in judd.m incorporates advanced statistical estimation techniques for improved dimensional calculations. When applying these algorithms, appropriate selection and parameter adjustment should be made based on specific data characteristics and analytical requirements. The corrint.m implementation typically requires setting appropriate distance thresholds, while gka.m involves kernel bandwidth optimization. In practical applications, considerations must be given to computational complexity, algorithm stability, and convergence properties to ensure the accuracy and reliability of calculation results. Proper initialization and parameter tuning in these MATLAB implementations are crucial for obtaining meaningful dimension estimates.