Orthogonal Basis

Orthogonal bases, sets of vectors that are mutually perpendicular, are fundamental tools for representing data and solving problems across diverse scientific fields. Current research focuses on developing and applying orthogonal bases in various contexts, including improving the efficiency and accuracy of machine learning models (e.g., through optimized piecewise polynomial approximations and novel positional encodings in transformers), enhancing signal processing techniques (e.g., in single-pixel imaging and matrix factorization), and addressing challenges in shape matching and other geometric problems. The development and application of orthogonal bases are crucial for advancing numerous fields, from improving the performance of algorithms to enabling new capabilities in areas like medical image analysis and robotics.