A stable multi-scale kernel for topological machine learning Conference Paper

Author(s): Reininghaus, Jan; Huber, Stefan; Bauer, Ulrich; Kwitt, Roland
Title: A stable multi-scale kernel for topological machine learning
Affiliation IST Austria
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.
Conference Title: CVPR: Computer Vision and Pattern Recognition
Conference Dates: June 7-12, 2015
Conference Location: 07-12-June-2015
Publisher: IEEE  
Date Published: 2015-10-14
Start Page: 4741
End Page: 4748
DOI: 10.1109/CVPR.2015.7299106
Open access: yes (repository)
IST Austria Authors
  1. Ulrich Bauer
    12 Bauer
  2. Stefan Huber
    11 Huber
Related IST Austria Work