Effectiveness of High-Dimensional Distance Metrics on Solar Flare Time Series

Abstract

Solar-flare forecasting has been extensively researched yet remains an open problem. In this paper, we investigate the contributions of elastic distance measures for detecting patterns in the solar-flare dataset, SWAN-SF. We employ a simple $k$-medoids clustering algorithm to evaluate the effectiveness of advanced, high-dimensional distance metrics. Our results show that, despite thorough optimization, none of the elastic distances outperform Euclidean distance by a significant margin. We demonstrate that, although elastic measures have shown promise for univariate time series, when applied to the multivariate time series of SWAN-SF, characterized by the high stochasticity of solar activity, they effectively collapse to Euclidean distance. We conduct thousands of experiments and present both quantitative and qualitative evidence supporting this finding.