A Stable Multi-Scale Kernel for Topological Machine Learning

Jan Reininghaus, Stefan Huber, Ulrich Bauer, Roland Kwitt

CVPR 2015

doi:10.1109/CVPR.2015.7299106 /cvpr/2015/reininghaus2015cvpr-stable/

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.

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Cite

Text

Reininghaus et al. "A Stable Multi-Scale Kernel for Topological Machine Learning." Conference on Computer Vision and Pattern Recognition, 2015. doi:10.1109/CVPR.2015.7299106

Markdown

[Reininghaus et al. "A Stable Multi-Scale Kernel for Topological Machine Learning." Conference on Computer Vision and Pattern Recognition, 2015.](https://mlanthology.org/cvpr/2015/reininghaus2015cvpr-stable/) doi:10.1109/CVPR.2015.7299106

BibTeX

@inproceedings{reininghaus2015cvpr-stable,
  title     = {{A Stable Multi-Scale Kernel for Topological Machine Learning}},
  author    = {Reininghaus, Jan and Huber, Stefan and Bauer, Ulrich and Kwitt, Roland},
  booktitle = {Conference on Computer Vision and Pattern Recognition},
  year      = {2015},
  doi       = {10.1109/CVPR.2015.7299106},
  url       = {https://mlanthology.org/cvpr/2015/reininghaus2015cvpr-stable/}
}