{"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/capacity-preserving-mapping-for-high","title":"Capacity Preserving Mapping for High-dimensional Data Visualization","arxiv_id":"1909.13322","date":"2019-09-29","proceeding":null,"authors":["Rongrong Wang","Xiaopeng Zhang"],"abstract":"We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls, our method makes right enough room to prepare for the embedding. A key component of the proposed method is an estimation of the correlation dimension at various scales which reflects the data density variation. The proposed adjustment to the capacity applies to any distance (Euclidean, geodesic, diffusion) and can potentially be used in many existing methods to mitigate the crowding during the dimension reduction. We demonstrate the effectiveness of the new method using synthetic and real datasets.","url_abs":"https://arxiv.org/abs/1909.13322v2","url_pdf":"https://arxiv.org/pdf/1909.13322v2.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":"capacity-preserving-mapping-for-high","repo_url":"https://github.com/rrwng/CPM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"data-visualization","task_name":"Data Visualization"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}