AATRN Watch Party: Ellipsoid Complexes and Their Stability

In this talk, I will introduce the Rips-type ellipsoid complex—a geometrically informed variant of the classical Rips complex. Instead of using Euclidean balls, we construct the complex from ellipsoids whose axes align with tangent directions estimated from the data via PCA. I will present a stability result showing that small perturbations of a point cloud lead to controlled changes in the resulting barcodes. Finally, I will describe experiments on datasets from Turkeš, Montúfar, and Otter [TMO22], where ellipsoid barcodes outperform both the Rips and alpha complexes in classification tasks.