{"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/compressive-spectral-embedding-sidestepping","title":"Compressive spectral embedding: sidestepping the SVD","arxiv_id":"1509.08360","date":"2015-09-28","proceeding":"NeurIPS 2015 12","authors":["Dinesh Ramasamy","Upamanyu Madhow"],"abstract":"Spectral embedding based on the Singular Value Decomposition (SVD) is a\nwidely used \"preprocessing\" step in many learning tasks, typically leading to\ndimensionality reduction by projecting onto a number of dominant singular\nvectors and rescaling the coordinate axes (by a predefined function of the\nsingular value). However, the number of such vectors required to capture\nproblem structure grows with problem size, and even partial SVD computation\nbecomes a bottleneck. In this paper, we propose a low-complexity it compressive\nspectral embedding algorithm, which employs random projections and finite order\npolynomial expansions to compute approximations to SVD-based embedding. For an\nm times n matrix with T non-zeros, its time complexity is O((T+m+n)log(m+n)),\nand the embedding dimension is O(log(m+n)), both of which are independent of\nthe number of singular vectors whose effect we wish to capture. To the best of\nour knowledge, this is the first work to circumvent this dependence on the\nnumber of singular vectors for general SVD-based embeddings. The key to\nsidestepping the SVD is the observation that, for downstream inference tasks\nsuch as clustering and classification, we are only interested in using the\nresulting embedding to evaluate pairwise similarity metrics derived from the\neuclidean norm, rather than capturing the effect of the underlying matrix on\narbitrary vectors as a partial SVD tries to do. Our numerical results on\nnetwork datasets demonstrate the efficacy of the proposed method, and motivate\nfurther exploration of its application to large-scale inference tasks.","url_abs":"http://arxiv.org/abs/1509.08360v1","url_pdf":"http://arxiv.org/pdf/1509.08360v1.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":"compressive-spectral-embedding-sidestepping","repo_url":"https://bitbucket.org/dineshkr/fastembed","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}