{"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/uncertainty-aware-principal-component","title":"Uncertainty-Aware Principal Component Analysis","arxiv_id":"1905.01127","date":"2019-05-03","proceeding":null,"authors":["Jochen Görtler","Thilo Spinner","Dirk Streeb","Daniel Weiskopf","Oliver Deussen"],"abstract":"We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach.","url_abs":"https://arxiv.org/abs/1905.01127v4","url_pdf":"https://arxiv.org/pdf/1905.01127v4.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":"uncertainty-aware-principal-component","repo_url":"https://github.com/grtlr/uapca","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"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}