{"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/perturbation-robust-representations-of","title":"Perturbation Robust Representations of Topological Persistence Diagrams","arxiv_id":"1807.10400","date":"2018-07-26","proceeding":"ECCV 2018 9","authors":["Anirudh Som","Kowshik Thopalli","Karthikeyan Natesan Ramamurthy","Vinay Venkataraman","Ankita Shukla","Pavan Turaga"],"abstract":"Topological methods for data analysis present opportunities for enforcing\ncertain invariances of broad interest in computer vision, including view-point\nin activity analysis, articulation in shape analysis, and measurement\ninvariance in non-linear dynamical modeling. The increasing success of these\nmethods is attributed to the complementary information that topology provides,\nas well as availability of tools for computing topological summaries such as\npersistence diagrams. However, persistence diagrams are multi-sets of points\nand hence it is not straightforward to fuse them with features used for\ncontemporary machine learning tools like deep-nets. In this paper we present\ntheoretically well-grounded approaches to develop novel perturbation robust\ntopological representations, with the long-term view of making them amenable to\nfusion with contemporary learning architectures. We term the proposed\nrepresentation as Perturbed Topological Signatures, which live on a Grassmann\nmanifold and hence can be efficiently used in machine learning pipelines. We\nexplore the use of the proposed descriptor on three applications: 3D shape\nanalysis, view-invariant activity analysis, and non-linear dynamical modeling.\nWe show favorable results in both high-level recognition performance and\ntime-complexity when compared to other baseline methods.","url_abs":"http://arxiv.org/abs/1807.10400v1","url_pdf":"http://arxiv.org/pdf/1807.10400v1.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":"perturbation-robust-representations-of","repo_url":"https://github.com/anirudhsom/Perturbed-Topological-Signature","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.10400","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1807.10400"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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