{"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/multi-set-canonical-correlation-analysis","title":"Multi-set Canonical Correlation Analysis simply explained","arxiv_id":"1802.03759","date":"2018-02-11","proceeding":null,"authors":["Lucas C. Parra"],"abstract":"There are a multitude of methods to perform multi-set correlated component\nanalysis (MCCA), including some that require iterative solutions. The methods\ndiffer on the criterion they optimize and the constraints placed on the\nsolutions. This note focuses perhaps on the simplest version, which can be\nsolved in a single step as the eigenvectors of matrix ${\\bf D}^{-1} {\\bf R}$.\nHere ${\\bf R}$ is the covariance matrix of the concatenated data, and ${\\bf D}$\nis its block-diagonal. This note shows that this solution maximizes inter-set\ncorrelation (ISC) without further constraints. It also relates the solution to\na two step procedure, which first whitens each dataset using PCA, and then\nperforms an additional PCA on the concatenated and whitened data. Both these\nsolutions are known, although a clear derivation and simple implementation are\nhard to find. This short note aims to remedy this.","url_abs":"http://arxiv.org/abs/1802.03759v1","url_pdf":"http://arxiv.org/pdf/1802.03759v1.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":"multi-set-canonical-correlation-analysis","repo_url":"https://github.com/lcparra/mcca","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}