{"acknowledgement":"The original work behind this article was developed for HE’s master’s thesis, supervised by RT. We are mostly in debt to César Camacho, who was HE’s co-advisor, as well as the members of the thesis jury, Clément Maria, Eduardo Mendes, and Jameson Cahill, not only for agreeing to evaluate the original work but also for many valuable inputs. Finally, we are indebted to the anonymous reviewers for their important feedback and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria).","status":"public","doi":"10.1007/s10208-025-09728-4","type":"journal_article","oa":1,"publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"department":[{"_id":"UlWa"}],"abstract":[{"text":"We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum of irreducible representations. Moreover, the knowledge of the representation type permits the reconstruction of its orbit, which is useful for identifying the Lie group that generates the action, from a finite list of candidates. Our algorithm is general for any compact Lie group, but only instantiations for SO(2), T^d, SU(2), and SO(3) are considered. Theoretical guarantees of robustness in terms of Hausdorff and Wasserstein distances are derived. Our tools are drawn from geometric measure theory, computational geometry, and optimization on matrix manifolds. The algorithm is tested for synthetic data up to dimension 32, as well as real-life applications in image analysis, harmonic analysis, density estimation, equivariant neural networks, chemical conformational spaces, and classical mechanics systems, achieving very accurate results.","lang":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"20407","date_published":"2025-09-15T00:00:00Z","quality_controlled":"1","author":[{"last_name":"Ennes","full_name":"Ennes, Henrique","first_name":"Henrique"},{"orcid":"0000-0002-1404-1095","full_name":"Tinarrage, Raphaël","first_name":"Raphaël","last_name":"Tinarrage","id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e"}],"PlanS_conform":"1","date_created":"2025-09-28T22:01:27Z","isi":1,"month":"09","corr_author":"1","publisher":"Springer Nature","oa_version":"Published Version","year":"2025","citation":{"chicago":"Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation Orbits of Compact Lie Groups from Point Clouds.” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s10208-025-09728-4\">https://doi.org/10.1007/s10208-025-09728-4</a>.","ieee":"H. Ennes and R. Tinarrage, “LieDetect: Detection of representation orbits of compact Lie groups from point clouds,” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2025.","mla":"Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation Orbits of Compact Lie Groups from Point Clouds.” <i>Foundations of Computational Mathematics</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s10208-025-09728-4\">10.1007/s10208-025-09728-4</a>.","ama":"Ennes H, Tinarrage R. LieDetect: Detection of representation orbits of compact Lie groups from point clouds. <i>Foundations of Computational Mathematics</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s10208-025-09728-4\">10.1007/s10208-025-09728-4</a>","apa":"Ennes, H., &#38; Tinarrage, R. (2025). LieDetect: Detection of representation orbits of compact Lie groups from point clouds. <i>Foundations of Computational Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-025-09728-4\">https://doi.org/10.1007/s10208-025-09728-4</a>","ista":"Ennes H, Tinarrage R. 2025. LieDetect: Detection of representation orbits of compact Lie groups from point clouds. Foundations of Computational Mathematics.","short":"H. Ennes, R. Tinarrage, Foundations of Computational Mathematics (2025)."},"OA_type":"hybrid","title":"LieDetect: Detection of representation orbits of compact Lie groups from point clouds","scopus_import":"1","arxiv":1,"date_updated":"2025-09-30T14:44:53Z","publication":"Foundations of Computational Mathematics","main_file_link":[{"url":"https://doi.org/10.1007/s10208-025-09728-4","open_access":"1"}],"publication_status":"epub_ahead","OA_place":"publisher","article_type":"original","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"external_id":{"isi":["001571197200001"],"arxiv":["2309.03086"]},"day":"15"}