Elastic Metric

Elastic metrics are distance measures designed to account for variations in shape, timing, or other transformations when comparing data points, particularly in complex spaces like those representing curves or surfaces. Current research focuses on developing and applying these metrics in various domains, including shape analysis (using methods like basis-restricted elastic shape analysis), time series event detection (with novel metrics like SoftED), and dimensionality reduction (integrating elastic measures into techniques such as t-SNE and UMAP). Improved accuracy in tasks such as shape registration, regression on curve manifolds, and time series clustering demonstrates the value of elastic metrics, offering more robust and informative analyses compared to traditional Euclidean approaches.