CUR Decomposition

CUR decomposition is a matrix factorization technique that approximates a large matrix using a smaller subset of its rows and columns, along with a smaller, connecting matrix. Current research focuses on extending CUR to tensors (multi-dimensional arrays) and integrating it into various applications, including low-rank tensor completion, efficient k-NN search with cross-encoders, and robust principal component analysis. These advancements aim to improve computational efficiency and scalability in diverse fields like machine learning, signal processing, and computer vision, particularly for handling high-dimensional data. The resulting algorithms often offer significant speedups and improved accuracy compared to traditional methods.