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

TL;DR

This study evaluates various high-dimensional elastic distance metrics for solar flare time series classification, finding they do not outperform Euclidean distance in multivariate, stochastic solar flare data.

Contribution

It systematically compares elastic and Euclidean distances on solar flare data, revealing elastic measures' limitations in high-dimensional, stochastic multivariate time series.

Findings

Elastic distances do not outperform Euclidean distance.

Elastic measures collapse to Euclidean in high-dimensional, stochastic data.

Thorough experiments support the limited effectiveness of elastic distances.

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.