Orthonormal Basis

Orthonormal bases, sets of mutually orthogonal and normalized vectors, are fundamental in various fields, serving as efficient representations for data and facilitating mathematical analysis. Current research focuses on developing and analyzing algorithms for constructing and utilizing orthonormal bases in diverse contexts, including deep learning (e.g., through Riemannian gradient descent on Stiefel manifolds), signal processing (e.g., via spectral transforms and diffusion maps), and machine learning (e.g., employing singular value decomposition for dimensionality reduction and feature learning). This work addresses challenges such as noise robustness, computational efficiency, and theoretical guarantees for convergence and accuracy, ultimately impacting fields ranging from image processing and communication systems to tensor recovery and graph embedding.