Metric Tensor

A metric tensor defines a way to measure distances and angles within a space, generalizing the familiar Euclidean distance to more complex geometries. Current research focuses on developing efficient algorithms for metric learning and optimization, particularly within the context of dimensionality reduction and manifold learning, employing techniques like optimal transport and hierarchical linear programming. These advancements have implications for diverse fields, improving the accuracy and efficiency of machine learning models, enhancing data analysis in areas such as network analysis and trajectory inference, and offering new approaches to solving optimization problems in high-dimensional spaces.