Discovering new relationships using multipoles through correlation and threshold analysis

Uncovering novel relationships in time series data is crucial for understanding complex systems. Traditional methods, such as linear regression and frequency domain analysis, often fail to capture the complex, non-linear interactions present in time series data. Multipoles represent a new class of linear relationships among multiple time series, where each series significantly contributes to the overall linear dependence. In this paper, we demonstrate the utility of multipoles in climate science and neuroscience, revealing meaningful patterns and interactions. The proposed approach transforms time series data into a multipole representation, decomposing it into multipolar components to detect intricate dependencies typically obscured by conventional techniques. This work uses scalable algorithms for efficient multipole transformation and analysis, validated through experiments on real-world datasets. Experimental results using climate data and blood pressure data show the significance in detecting hidden patterns and understanding underlying correlations helping us map relationships between the relevant parameters. In climatic time series, our method uncovers weather dynamics with threshold values, while in healthcare, it reveals complex interactions between physiological parameters demonstrating graphical results. This paper contributes a novel perspective on time series analysis, enriching the analytical toolbox for researchers and practitioners, and offers a promising direction for exploring complex data relationships in various domains, including climate science and neuroscience.