{"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/bayesian-inference-for-pca-and-music","title":"Bayesian inference for PCA and MUSIC algorithms with unknown number of sources","arxiv_id":"1809.10168","date":"2018-09-26","proceeding":null,"authors":["Viet Hung Tran","Wenwu Wang"],"abstract":"Principal component analysis (PCA) is a popular method for projecting data\nonto uncorrelated components in lower dimension, although the optimal number of\ncomponents is not specified. Likewise, multiple signal classification (MUSIC)\nalgorithm is a popular PCA-based method for estimating directions of arrival\n(DOAs) of sinusoidal sources, yet it requires the number of sources to be known\na priori. The accurate estimation of the number of sources is hence a crucial\nissue for performance of these algorithms. In this paper, we will show that\nboth PCA and MUSIC actually return the exact joint maximum-a-posteriori (MAP)\nestimate for uncorrelated steering vectors, although they can only compute this\nMAP estimate approximately in correlated case. We then use Bayesian method to,\nfor the first time, compute the MAP estimate for the number of sources in PCA\nand MUSIC algorithms. Intuitively, this MAP estimate corresponds to the highest\nprobability that signal-plus-noise's variance still dominates projected noise's\nvariance on signal subspace. In simulations of overlapping multi-tone sources\nfor linear sensor array, our exact MAP estimate is far superior to the\nasymptotic Akaike information criterion (AIC), which is a popular method for\nestimating the number of components in PCA and MUSIC algorithms.","url_abs":"http://arxiv.org/abs/1809.10168v1","url_pdf":"http://arxiv.org/pdf/1809.10168v1.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":"bayesian-inference-for-pca-and-music","repo_url":"https://github.com/VietTran86/PCA_MUSIC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}