Correlation of divergency: c-delta. Being different in a similar way or not (2510.16717v1)

Abstract: This paper introduces the correlation-of-divergency coefficient, c-delta, a custom statistical measure designed to quantify the similarity of internal divergence patterns between two groups of values. Unlike conventional correlation coefficients such as Pearson or Spearman, which assess the association between paired values, c-delta evaluates whether the way values differ within one group is mirrored in another. The method involves calculating, for each value, its divergence from all other values in its group, and then comparing these patterns across the two groups (e.g., human vs machine intelligence). The coefficient is normalised by the average root mean square divergence within each group, ensuring scale invariance. Potential applications of c-delta span quantum physics, where it can compare the spread of measurement outcomes between quantum systems, as well as fields such as genetics, ecology, psychometrics, manufacturing, machine learning, and social network analysis. The measure is particularly useful for benchmarking, clustering validation, and assessing the similarity of variability structures. While c-delta is not bounded between -1 and 1 and may be sensitive to outliers (but so is PMCC), it offers a new perspective for analysing internal variability and divergence. The article discusses the mathematical formulation, potential adaptations for complex data, and the interpretative considerations relevant to this alternative approach.