Symmetric Positive Definite

Symmetric positive definite (SPD) matrices, representing covariance and other types of positive-definite relationships, are increasingly important in machine learning and related fields. Current research focuses on developing efficient algorithms and neural network architectures, such as those based on Riemannian geometry and denoising diffusion probabilistic models (DDPMs), for processing and learning from SPD-valued data, often leveraging techniques like tangent space mapping and specialized Riemannian metrics. This work is driven by the need for effective handling of SPD data in diverse applications, including structural health monitoring, image analysis, and brain-computer interfaces, where SPD matrices offer advantages in representing complex relationships and correlations. The development of robust and efficient methods for SPD data processing is thus crucial for advancing these fields.