A Stable Multi-Scale Kernel for Topological Machine Learning
Abstract
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. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.
Cite
@article{arxiv.1412.6821,
title = {A Stable Multi-Scale Kernel for Topological Machine Learning},
author = {Jan Reininghaus and Stefan Huber and Ulrich Bauer and Roland Kwitt},
journal= {arXiv preprint arXiv:1412.6821},
year = {2014}
}