Provable kernel methods for point-cloud and graph classification.

Research · Plate VI
Topological Kernels for Machine Learning
Provable kernel methods for point-cloud and graph classification Three collaborators Updated MMXXVI
Two classes of points separated by a hyperplane in feature space; the topological kernel embeds each point cloud as a vector before the linear classifier sees it.
Two classes, each a point cloud, mapped through a topological kernel into a feature space where a linear classifier suffices.
“A kernel that classifies but cannot be argued with is a kernel that has not been understood. The work is in writing the guarantees down.”

The setting: a point cloud or a graph carries topological signal—connectedness, loops, voids—that ordinary descriptors quietly discard. A line of work, with Atish Mitra, Žiga Virk, and Pramita Bagchi, aims to put topological data analysis on the same theoretical footing as kernel methods in machine learning. The kernels are closed-form, the landmarks are chosen with care, and the resulting classifiers come with proofs of stability, expressivity, and sample complexity.

The recurring shape: define a kernel that reads topological signal through carefully chosen landmarks, evaluate it in closed form, and certify the downstream classifier. The certification is the point. Without it, what one has is a useful classifier; with it, a usable theorem.

Recent preprints

Filed under Theory · Open Problems Two preprints, MMXXVI

Collaborators

Filed under Co-authors Three institutions, three countries
  • Atish Mitra, Montana Technological University
  • Žiga Virk, University of Ljubljana
  • Pramita Bagchi, George Mason University