Symmetric Space

Symmetric spaces, possessing inherent geometric structures beyond Euclidean space, are increasingly used in data analysis and machine learning to model complex, non-linear data. Current research focuses on developing and applying neural network architectures tailored to these spaces, such as those leveraging symmetric positive definite matrices or hyperbolic geometry, along with associated kernel methods and Gaussian processes. This work aims to improve the accuracy and efficiency of algorithms by better aligning the underlying geometry of the data with the model's structure, leading to advancements in areas like graph analysis and human activity recognition. The resulting models offer improved performance compared to Euclidean-based approaches for handling data with intricate relationships and non-uniform structures.