{"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/nested-subspace-arrangement-for","title":"Nested Subspace Arrangement for Representation of Relational Data","arxiv_id":"2007.02007","date":"2020-07-04","proceeding":"ICML 2020 1","authors":["Nozomi Hata","Shizuo Kaji","Akihiro Yoshida","Katsuki Fujisawa"],"abstract":"Studies on acquiring appropriate continuous representations of discrete objects, such as graphs and knowledge base data, have been conducted by many researchers in the field of machine learning. In this study, we introduce Nested SubSpace (NSS) arrangement, a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as special cases of the NSS arrangement. Based on the concept of the NSS arrangement, we implement a Disk-ANChor ARrangement (DANCAR), a representation learning method specialized to reproducing general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${\\mathbb R}^{20}$ with an F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization in understanding the characteristics of graphs.","url_abs":"https://arxiv.org/abs/2007.02007v1","url_pdf":"https://arxiv.org/pdf/2007.02007v1.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":"nested-subspace-arrangement-for","repo_url":"https://github.com/KyushuUniversityMathematics/DANCAR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2007.02007","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2007.02007"}},"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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