Topological Kernels for Machine Learning

Provable kernel methods for point-cloud and graph classification.

A line of work, with Atish Mitra, Žiga Virk, and Pramita Bagchi, aiming to put topological data analysis on the same theoretical footing as kernel methods in machine learning.

The setting: a point cloud or a graph carries topological signal—connectedness, loops, voids—that ordinary descriptors discard. We design closed-form, certified kernels that read this signal through carefully chosen landmarks, and we prove guarantees on the resulting classifiers (stability, expressivity, sample complexity).

The recent preprints introduce two such kernels:

• A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification—an adaptive landmark scheme with closed-form kernel evaluation, submitted to Foundations of Computational Mathematics.
• A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification—a persistence-based variant, submitted to Journal of Machine Learning Research.

Collaborators

• Atish Mitra, Montana Technological University
• Žiga Virk, University of Ljubljana
• Pramita Bagchi, George Mason University