{"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/the-all0core-tensor-decomposition-for-sparse","title":"The AL$\\ell_0$CORE Tensor Decomposition for Sparse Count Data","arxiv_id":"2403.06153","date":"2024-03-10","proceeding":null,"authors":["John Hood","Aaron Schein"],"abstract":"This paper introduces AL$\\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\\ell_0$CORE is a Tucker decomposition where the number of non-zero elements (i.e., the $\\ell_0$-norm) of the core tensor is constrained to a preset value $Q$ much smaller than the size of the core. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. AL$\\ell_0$CORE -- i.e., $allo$cated $\\ell_0$-$co$nstrained $core$-- thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\\ell_0$CORE typically requires only tiny fractions (e.g.,~1%) of the full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.","url_abs":"https://arxiv.org/abs/2403.06153v2","url_pdf":"https://arxiv.org/pdf/2403.06153v2.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":"the-all0core-tensor-decomposition-for-sparse","repo_url":"https://github.com/jhood3/allocore","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[{"method_slug":"tucker","method_name":"TuckER"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}