{"abstract":[{"text":"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.","lang":"eng"}],"month":"10","oa":1,"publist_id":"5709","author":[{"last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","first_name":"Jan"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"date_updated":"2021-01-12T06:51:03Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"date_created":"2018-12-11T11:52:17Z","date_published":"2015-10-14T00:00:00Z","page":"4741 - 4748","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"publication_status":"published","_id":"1483","day":"14","status":"public","doi":"10.1109/CVPR.2015.7299106","conference":{"name":"CVPR: Computer Vision and Pattern Recognition","location":"Boston, MA, USA","start_date":"2015-06-07","end_date":"2015-06-12"},"publisher":"IEEE","citation":{"ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>","mla":"Reininghaus, Jan, et al. <i>A Stable Multi-Scale Kernel for Topological Machine Learning</i>. IEEE, 2015, pp. 4741–48, doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., &#38; Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>."},"type":"conference","year":"2015","language":[{"iso":"eng"}],"scopus_import":1,"oa_version":"Preprint","title":"A stable multi-scale kernel for topological machine learning"}