Exploration and Deconstruction of Correlation Cycles in Multidimensional Datasets

Correlation analysis is one of the most prolific statistical methods used in data analysis problems, mining of knowledge focused on relationships of attributes in large datasets, and in various predictive tasks utilizing statistical, machine learning, and deep learning models. This approach to the analysis of functional relationships in multidimensional datasets is commonly used in conjunction with visual analysis approaches, which offer novel context for the relationships in data and clarify the results presented in large correlation matrices. One of such visualization methods uses graphical models called correlation graphs and chains, which visualize individual direct and indirect relationships between pairs of attributes in a dataset of interest as a graph structure, where vertices of the graph represent attributes of the dataset and edges between vertices represent the correlation of these attributes. This work focuses on the definition, identification, and exploration of so-called correlation cycles, which can be-through their deconstruction-used as an approach to lower error values in regression tasks. After the implementation of the correlation cycle identification and deconstruction, the proposed concept is evaluated on predictive analysis tasks in the context of three benchmarking datasets from the engineering field-the Sensor dataset, Superconductivity dataset, and Energy Farm dataset. The results obtained in this study show that when using simple, explainable regressors, the method utilizing deconstructed correlation cycles reaches a lower error rate in 83.3% of regression cases compared to the same regression models without the cycle incorporation.