{"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/sheaves-a-topological-approach-to-big-data","title":"Sheaves: A Topological Approach to Big Data","arxiv_id":"1901.01341","date":"2019-01-04","proceeding":null,"authors":["Linas Vepstas"],"abstract":"This document develops general concepts useful for extracting knowledge\nembedded in large graphs or datasets that have pair-wise relationships, such as\ncause-effect-type relations. Almost no underlying assumptions are made, other\nthan that the data can be presented in terms of pair-wise relationships between\nobjects/events. This assumption is used to mine for patterns in the dataset,\ndefining a reduced graph or dataset that boils-down or concentrates information\ninto a more compact form. The resulting extracted structure or set of patterns\nare manifestly symbolic in nature, as they capture and encode the graph\nstructure of the dataset in terms of a (generative) grammar. This structure is\nidentified as having the formal mathematical structure of a sheaf. In essence,\nthis paper introduces the basic concepts of sheaf theory into the domain of\ngraphical datasets.","url_abs":"http://arxiv.org/abs/1901.01341v1","url_pdf":"http://arxiv.org/pdf/1901.01341v1.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":"sheaves-a-topological-approach-to-big-data","repo_url":"https://github.com/arquicanedo/graph2sheaves","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1901.01341","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}