{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deep-learning-with-topological-signatures","title":"Deep Learning with Topological Signatures","arxiv_id":"1707.04041","date":"2017-07-13","proceeding":"NeurIPS 2017 12","authors":["Christoph Hofer","Roland Kwitt","Marc Niethammer","Andreas Uhl"],"abstract":"Inferring topological and geometrical information from data can offer an\nalternative perspective on machine learning problems. Methods from topological\ndata analysis, e.g., persistent homology, enable us to obtain such information,\ntypically in the form of summary representations of topological features.\nHowever, such topological signatures often come with an unusual structure\n(e.g., multisets of intervals) that is highly impractical for most machine\nlearning techniques. While many strategies have been proposed to map these\ntopological signatures into machine learning compatible representations, they\nsuffer from being agnostic to the target learning task. In contrast, we propose\na technique that enables us to input topological signatures to deep neural\nnetworks and learn a task-optimal representation during training. Our approach\nis realized as a novel input layer with favorable theoretical properties.\nClassification experiments on 2D object shapes and social network graphs\ndemonstrate the versatility of the approach and, in case of the latter, we even\noutperform the state-of-the-art by a large margin.","url_abs":"http://arxiv.org/abs/1707.04041v3","url_pdf":"http://arxiv.org/pdf/1707.04041v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"deep-learning-with-topological-signatures","repo_url":"https://github.com/c-hofer/persistent_homology_toolbox","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"deep-learning-with-topological-signatures","repo_url":"https://github.com/c-hofer/nips2017","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"deep-learning-with-topological-signatures","repo_url":"https://github.com/billy-mosse/spiderman","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"deep-learning-with-topological-signatures","repo_url":"https://github.com/ssmele/CompTopoProg","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1707.04041","atlas_url":"https://app.syntology.ai/?focus=1707.04041","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}