Publications and preprints I have contributed to.
RotaTouille is a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution.
The core bifiltration is a parameter-free density-based bifiltration interleaved with the well-known multicover bifiltration. This makes it suitable for extracting topological features from noisy point cloud data. In particulat, both bifiltrations enjoy stability with respect to the Prohorov distance between the point measures. For point clouds in $\mathbb{R}^n$, a smaller and more efficient version based on the Delaunay complex also exists: The Delaunay Core bifiltration is implemented in the multipers library making it accessible to both researchers and practitioners.
For a quick start: check out the multipers documentation for a tutorial on how to use the Delaunay Core bifiltration in Python.
Relaxing the metric assumption in topological data analysis allows for the analysis of directed networks and asymmetric data. The monoidal Rips filtration is a generalization of the Vietoris-Rips filtration to weighted directed graphs. To allow for directed edges, we work with filtered simplicial sets instead of filtered simplicial complexes. We also allow values in a class of lattices, which includes both the real numbers and products of totally ordered sets. This makes our construction applicable to both single-parameter and multiparameter persistence. We introduce a generalized network distance, and prove stability results for the persistent homology of the monoidal Rips filtration with respect to this distance.
The ICML 2023 Topological Deep Learning Challenge was a competition that aimed to benchmark and promote the implementation of topological deep learning methods. I implemented the SCoNe layer from the paper “Principled Simplicial Neural Networks for Trajectory Prediction” as part of this challenge, and placed second in the simplicial complex category. The implementation is now part of the TopoModelX library, and a tutorial notebook is available in the TopoModelX documentation.
The TopoX implementation paper describing the three packages: TopoNetX, TopoEmbedX and TopoModelX enabling machine learning on topological domains that extend graphs such as hypergraphs, simplicial, cellular, path and combinatorial complexes.