Correlation Dimension Calculation Results Using GP Algorithm

This document introduces a key concept - correlation dimension. To better understand this concept, we can elaborate on its technical implementation. Correlation dimension is a metric used to quantify the degree of association between data points within a dataset, commonly applied in data mining and machine learning domains. When computing correlation dimension, the GP (Genetic Programming) algorithm can be employed as an effective approach. The GP algorithm is an evolutionary computation technique that utilizes genetic operations (selection, crossover, mutation) to evolve mathematical expressions or programs that best fit the data structure. For implementing correlation dimension calculation, the algorithm typically involves these key steps: first, reconstructing the phase space using time-delay embedding methods; second, calculating the correlation integral through pairwise distance analysis; third, applying GP to optimize the dimension estimation function. The core implementation would include functions for population initialization, fitness evaluation based on correlation sums, and genetic operator applications. Through GP algorithm implementation, we obtain accurate correlation dimension results, enabling better understanding of intrinsic relationships between data points in complex datasets. The algorithm's strength lies in its ability to handle high-dimensional data efficiently while avoiding explicit model assumptions through its evolutionary optimization process.