Karhunen Lo\`eve Transform

The Karhunen-Loève Transform (KLT) is an optimal linear transform for data decorrelation and dimensionality reduction, finding applications in diverse fields from image processing to system identification. Current research focuses on improving KLT's efficiency and accuracy, particularly through hybrid model-based/data-driven approaches that combine the stability of pre-defined transforms with the adaptability of data-driven methods, and on developing low-complexity approximations for real-time applications. These advancements are impacting various domains, including image compression, uncertainty quantification in physical systems, and machine learning force field design, by enabling faster computations and improved model accuracy.