Measuring Graph Distance Using the Labeled Merge Tree Interleaving Distance

Learn about geometric graph analysis and distance measurement through a 48-minute research talk that introduces a novel metric for comparing geometric graphs using merge trees. Explore how to preserve crucial data information through directional transform-based rotation of sublevel sets and understand the implementation of a surjective multi-labeling scheme for merge tree representation. Discover two polynomial-time computation methods - sampling-based approximation and exact distance calculation using kinetic data structures. Follow along as the speaker demonstrates practical applications across two distinct datasets, showcasing how this approach can be applied to real-world scenarios like road networks, sensor networks, and molecular structures.