{"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/adagio-fast-data-aware-near-isometric-linear","title":"ADAGIO: Fast Data-aware Near-Isometric Linear Embeddings","arxiv_id":"1609.05388","date":"2016-09-17","proceeding":null,"authors":["Jarosław Błasiok","Charalampos E. Tsourakakis"],"abstract":"Many important applications, including signal reconstruction, parameter\nestimation, and signal processing in a compressed domain, rely on a\nlow-dimensional representation of the dataset that preserves {\\em all} pairwise\ndistances between the data points and leverages the inherent geometric\nstructure that is typically present. Recently Hedge, Sankaranarayanan, Yin and\nBaraniuk \\cite{hedge2015} proposed the first data-aware near-isometric linear\nembedding which achieves the best of both worlds. However, their method NuMax\ndoes not scale to large-scale datasets.\n  Our main contribution is a simple, data-aware, near-isometric linear\ndimensionality reduction method which significantly outperforms a\nstate-of-the-art method \\cite{hedge2015} with respect to scalability while\nachieving high quality near-isometries. Furthermore, our method comes with\nstrong worst-case theoretical guarantees that allow us to guarantee the quality\nof the obtained near-isometry. We verify experimentally the efficiency of our\nmethod on numerous real-world datasets, where we find that our method ($<$10\nsecs) is more than 3\\,000$\\times$ faster than the state-of-the-art method\n\\cite{hedge2015} ($>$9 hours) on medium scale datasets with 60\\,000 data points\nin 784 dimensions. Finally, we use our method as a preprocessing step to\nincrease the computational efficiency of a classification application and for\nspeeding up approximate nearest neighbor queries.","url_abs":"http://arxiv.org/abs/1609.05388v1","url_pdf":"http://arxiv.org/pdf/1609.05388v1.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":"adagio-fast-data-aware-near-isometric-linear","repo_url":"https://github.com/tsourolampis/Adagio","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}