Euclidean Space

Euclidean space, the familiar setting of classical geometry, remains a cornerstone of many scientific fields, but its limitations are increasingly driving research into alternative geometric frameworks. Current research focuses on developing and refining algorithms for tasks like clustering (e.g., k-means, k-median) and deep metric learning within Euclidean space, often incorporating techniques like coresets for improved scalability and warped softmax functions for enhanced performance. However, a significant trend involves exploring non-Euclidean geometries, such as hyperbolic space, to better represent hierarchical or complex data structures, particularly in machine learning applications like image generation and graph embedding, highlighting the need for adaptable methods that transcend the Euclidean paradigm.