{"status":"public","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"}],"_id":"1483","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"day":"14","page":"4741 - 4748","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"type":"conference","author":[{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan"},{"first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"},{"first_name":"Ulrich","full_name":"Bauer, Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"first_name":"Roland","full_name":"Kwitt, Roland","last_name":"Kwitt"}],"publisher":"IEEE","date_created":"2018-12-11T11:52:17Z","date_updated":"2021-01-12T06:51:03Z","conference":{"name":"CVPR: Computer Vision and Pattern Recognition","location":"Boston, MA, USA","start_date":"2015-06-07","end_date":"2015-06-12"},"language":[{"iso":"eng"}],"title":"A stable multi-scale kernel for topological machine learning","year":"2015","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"oa":1,"oa_version":"Preprint","scopus_import":1,"publist_id":"5709","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.","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.","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.","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>","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>.","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>"},"doi":"10.1109/CVPR.2015.7299106","month":"10","publication_status":"published","date_published":"2015-10-14T00:00:00Z"}