A Stable Multi-Scale Kernel for Topological Machine Learning
Jan Reininghaus, Stefan Huber, Ulrich Bauer, Roland Kwitt
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.
BibTeX
@inproceedings{cvpr2015_astablemultiscal,
title = {A Stable Multi-Scale Kernel for Topological Machine Learning},
author = {Jan Reininghaus and Stefan Huber and Ulrich Bauer and Roland Kwitt},
booktitle = {CVPR 2015},
year = {2015}
}