{"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/correlated-components-analysis-extracting","title":"Correlated Components Analysis - Extracting Reliable Dimensions in Multivariate Data","arxiv_id":"1801.08881","date":"2018-01-26","proceeding":null,"authors":["Lucas C. Parra","Stefan Haufe","Jacek P. Dmochowski"],"abstract":"How does one find dimensions in multivariate data that are reliably expressed\nacross repetitions? For example, in a brain imaging study one may want to\nidentify combinations of neural signals that are reliably expressed across\nmultiple trials or subjects. For a behavioral assessment with multiple ratings,\none may want to identify an aggregate score that is reliably reproduced across\nraters. Correlated Components Analysis (CorrCA) addresses this problem by\nidentifying components that are maximally correlated between repetitions (e.g.\ntrials, subjects, raters). Here we formalize this as the maximization of the\nratio of between-repetition to within-repetition covariance. We show that this\ncriterion maximizes repeat-reliability, defined as mean over variance across\nrepeats, and that it leads to CorrCA or to multi-set Canonical Correlation\nAnalysis, depending on the constraints. Surprisingly, we also find that CorrCA\nis equivalent to Linear Discriminant Analysis for zero-mean signals, which\nprovides an unexpected link between classic concepts of multivariate analysis.\nWe present an exact parametric test of statistical significance based on the\nF-statistic for normally distributed independent samples, and present and\nvalidate shuffle statistics for the case of dependent samples. Regularization\nand extension to non-linear mappings using kernels are also presented. The\nalgorithms are demonstrated on a series of data analysis applications, and we\nprovide all code and data required to reproduce the results.","url_abs":"http://arxiv.org/abs/1801.08881v5","url_pdf":"http://arxiv.org/pdf/1801.08881v5.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":"correlated-components-analysis-extracting","repo_url":"https://github.com/lcparra/corrca","is_official":1,"mentioned_in_paper":0,"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}