{"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/collective-spectral-density-estimation-and","title":"Collective Spectral Density Estimation and Clustering for Spatially-Correlated Data","arxiv_id":"2007.14085","date":"2020-07-28","proceeding":null,"authors":["Tianbo Chen","Ying Sun","Mehdi Maadooliat"],"abstract":"In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to impose the smoothness of the estimated 2D-SDFs and the spatial dependence of the spatially-correlated subregions. The proposed technique provides a score matrix, that is comprised of the estimated coefficients associated with the common set of basis functions representing the 2D-SDFs. {Instead of clustering the estimated SDFs directly, we propose to employ the score matrix for clustering purposes, taking advantage of its low-dimensional property.} In a simulation study, we demonstrate that our proposed method outperforms other competing estimation procedures used for clustering. Finally, to validate the described clustering method, we apply the procedure to soil moisture data from the Mississippi basin to produce homogeneous spatial clusters. We produce animations to dynamically show the estimation procedure, including the estimated 2D-SDFs and the score matrix, which provide an intuitive illustration of the proposed method.","url_abs":"http://arxiv.org/abs/2007.14085v1","url_pdf":"http://arxiv.org/pdf/2007.14085v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"collective-spectral-density-estimation-and","repo_url":"https://github.com/tianbochen1/NCSDE_Spatial","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}