{"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/core-consistency-diagnosis-for-block-term","title":"Core consistency diagnosis for Block Term Decomposition in rank $(L_r, L_r, 1)$","arxiv_id":"2312.11151","date":"2023-12-18","proceeding":null,"authors":["Noramon Dron","Javier Escudero"],"abstract":"Determining the underlying number of components $R$ in tensor decompositions is challenging. Diverse techniques exist for various decompositions, notably the core consistency diagnostic (CORCONDIA) for Canonical Polyadic Decomposition (CPD). Here, we propose a model that intuitively adapts CORCONDIA for rank estimation in Block Term Decomposition (BTD) of rank $(L_r, L_r, 1)$: BTDCORCONDIA. Our metric was tested on simulated and real-world tensor data, including assessments of its sensitivity to noise and the indeterminacy of BTD $(L_r, L_r, 1)$. We found that selecting appropriate $R$ and $L_r$ led to core consistency reaching or close to 100%, and BTDCORCONDIA is efficient when the tensor has significantly more elements than the core. Our results confirm that CORCONDIA can be extended to BTD $(L_r, L_r, 1)$, and the resulting metric can assist in the process of determining the number of components in this tensor factorisation.","url_abs":"https://arxiv.org/abs/2312.11151v1","url_pdf":"https://arxiv.org/pdf/2312.11151v1.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":"core-consistency-diagnosis-for-block-term","repo_url":"https://github.com/noramondron/btdcorcondia","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"diagnostic","task_name":"Diagnostic"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}