A Stable Multi-Scale Kernel for Topological Machine Learning

Understand

Topological data analysis offers a rich source of valuable information to study vision problems.

• Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA.
• In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data.
• We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance.