Shaped by What's Missing: Topological Discovery of Behavioral Transitions

📅 Project Timeline: Mar 2025 - Now

Classical manifold learning methods (PCA, UMAP, t-SNE) learn a low-dimensional embedding of high-dimensional data. We take a different approach: instead of projecting to a coordinate space, we learn the topological skeleton of the data manifold itself. Each behavioral clip from a deep RL policy (MIMIC-MJX) is a trajectory in a high-dimensional temporal space. We reconstruct the discrete Morse graph of this point cloud to extract two types of structural primitives: DM Cycles (loops in the graph skeleton, capturing periodic or recurrent behavioral motifs) and DM Paths (edge-disjoint paths between persistent density minima, capturing transition corridors). These sub-trajectories are the learned manifold coordinates — they represent the intrinsic structure (loops, branches, connectivity) rather than just pairwise proximity. I am working on this with advising from professor Yusu Wang and professor Talmo Pereira. This work is currently under submission. TopoVNL was presented at the Annual Society for Neuroscience (SfN) 2025 Conference with this poster.

TopoMIMIC Repository