A New Method for Judging Nonlinear Correlation Based on Fusion Metrics

In the process of exploring the relationships between variables, correlation analysis, as a significant research tool, encounters two distinct types of challenges: linear and nonlinear correlations. Linear correlation describes the proportional relationship between variables, whereas nonlinear correlation uncovers more complex relationships that cannot be represented by linear equations. Given the widespread presence of nonlinear relationships in practice, it is essential to adopt suitable analytical methods. To effectively evaluate the degree of correlation between nonlinear variables, this paper proposes a fusion metric based on an enhanced cosine similarity and a weighted Mahalanobis distance. This method combines the directionality assessment of cosine similarity and the characteristics of the weighted Mahalanobis distance to provide a more comprehensive analysis of the similarities and differences between variables. Through this fusion measure, the changes in the degree of nonlinear correlation can be captured, allowing for the identification of potential var-iables with low correlation, and the results derived from the fusion measure align with the conclusions drawn from the mutual information method for assessing relevance. In conclusion, the fusion metric based on an enhanced cosine similarity and weighted Mahalanobis distance offers a novel method for analyzing the degree of nonlinear correlation, which is anticipated to be applicable in a broader range of applications.