Higher Order Singular Value Decomposition

Higher-order singular value decomposition (HOSVD) extends the familiar singular value decomposition (SVD) to handle multi-dimensional data like images and videos, aiming to efficiently represent and process this data using low-rank approximations. Current research focuses on applying HOSVD and its variants, such as Tucker decomposition and generalizations over finite-dimensional algebras, to improve various tasks including image denoising, plant disease detection, and emotion editing in generative models. These advancements offer significant improvements in data compression, dimensionality reduction, and the performance of algorithms across diverse applications, leading to more efficient and accurate solutions in image processing, machine learning, and other fields.