\Ell_p$ Distance

$\ell_p$ distances are a family of metrics used to quantify the dissimilarity between data points or probability distributions, finding applications across diverse fields. Current research focuses on developing computationally efficient algorithms, such as variants of the Sinkhorn algorithm for Wasserstein distances, and exploring the relationship between $\ell_p$ distances and other metrics like hyperbolicity for improved tree fitting and data analysis. These advancements are improving the robustness and scalability of distance calculations, leading to enhanced performance in machine learning tasks such as classification, clustering, and representation learning, particularly in the presence of noisy or high-dimensional data. The development of robust and efficient $\ell_p$ distance computations is crucial for advancing various fields, including topological data analysis and optimal transport.