Non-parametric correlation structures and their respective embeddings in predictive analysis

In data analysis, there is a natural connection between correlation and visual analysis. Correlation analysis enables the identification of relationships between attribute pairs in multidimensional datasets, while visual data analysis focuses on representing the data and the models that process it in a comprehensible visual form. A notable model that integrates these two approaches is the correlation structure—a graphical and visual model based on correlation graphs and correlation chains. However, traditional correlation structures are parametric, requiring an attribute of interest as an input to guide the analysis. This presents a major challenge when analyzing unfamiliar datasets or domains, where the attributes of interest are not known in advance. To address this limitation, this study proposes the design and implementation of non-parametric correlation structures—specifically, non-parametric correlation graphs and non-parametric correlation chains—that eliminate the dependency on predefined input attributes. These models are implemented in Python language to ensure broad accessibility and integration into existing data analysis pipelines. Once implemented, the concept of embedding non-parametric correlation chains within non-parametric correlation graphs is explored to enhance the interpretability of correlation structures of a dataset. The proposed approach is evaluated through case studies on five open-access datasets, varying in size from 6 to 149 attributes, and tested using five regression analysis models. Finally, the advantages and disadvantages of the proposed model are determined.