{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:25:40Z","timestamp":1787336740857,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100004488","name":"Croatian Science Foundation","doi-asserted-by":"crossref","award":["IP-2019-04-6268"],"award-info":[{"award-number":["IP-2019-04-6268"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-17-EURE-0010"],"award-info":[{"award-number":["ANR-17-EURE-0010"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P31881-N32"],"award-info":[{"award-number":["P31881-N32"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["VI.Vidi.195.141"],"award-info":[{"award-number":["VI.Vidi.195.141"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Invariant coordinate selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an independent component or a non-Gaussian component analysis method. The usual implementation of ICS is based on a joint diagonalization of two scatter matrices, and may be numerically unstable in some ill-conditioned situations. We focus on one-step M-scatter matrices and propose a new implementation of ICS based on a pivoted QR factorization of the centered data set. This factorization avoids the direct computation of the scatter matrices and their inverse and brings numerical stability to the algorithm. Furthermore, the row and column pivoting leads to a rank revealing procedure that allows computation of ICS when the scatter matrices are not full rank. Several artificial and real data sets illustrate the interest of using the new implementation compared to the original one.<\/jats:p>","DOI":"10.1137\/22m1498759","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T11:02:40Z","timestamp":1678446160000},"page":"97-121","source":"Crossref","is-referenced-by-count":7,"title":["Numerical Considerations and a new implementation for invariant coordinate selection"],"prefix":"10.1137","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6511-9091","authenticated-orcid":true,"given":"Aurore","family":"Archimbaud","sequence":"first","affiliation":[{"name":"Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zlatko","family":"Drma\u010d","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Klaus","family":"Nordhausen","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Jyv\u00e4skyl\u00e4, Jyv\u00e4skyl\u00e4, Finland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Una","family":"Radoji\u010di\u0107","sequence":"additional","affiliation":[{"name":"Institute of Statistics & Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anne","family":"Ruiz-Gazen","sequence":"additional","affiliation":[{"name":"Toulouse School of Economics, Universit\u00e9 Toulouse 1 Capitole, Toulouse, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.jmva.2016.08.007","volume":"152","author":"Alashwali F.","year":"2016","journal-title":"J. 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