{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T14:11:40Z","timestamp":1780063900262,"version":"3.54.0"},"reference-count":54,"publisher":"MIT Press - Journals","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2017,6]]},"abstract":"<jats:p> The estimation of covariance matrices is of prime importance to analyze the distribution of multivariate signals. In motor imagery\u2013based brain-computer interfaces (MI-BCI), covariance matrices play a central role in the extraction of features from recorded electroencephalograms (EEGs); therefore, correctly estimating covariance is crucial for EEG classification. This letter discusses algorithms to average sample covariance matrices (SCMs) for the selection of the reference matrix in tangent space mapping (TSM)\u2013based MI-BCI. Tangent space mapping is a powerful method of feature extraction and strongly depends on the selection of a reference covariance matrix. In general, the observed signals may include outliers; therefore, taking the geometric mean of SCMs as the reference matrix may not be the best choice. In order to deal with the effects of outliers, robust estimators have to be used. In particular, we discuss and test the use of geometric medians and trimmed averages (defined on the basis of several metrics) as robust estimators. The main idea behind trimmed averages is to eliminate data that exhibit the largest distance from the average covariance calculated on the basis of all available data. The results of the experiments show that while the geometric medians show little differences from conventional methods in terms of classification accuracy in the classification of electroencephalographic recordings, the trimmed averages show significant improvement for all subjects. <\/jats:p>","DOI":"10.1162\/neco_a_00963","type":"journal-article","created":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T18:47:22Z","timestamp":1492195642000},"page":"1631-1666","source":"Crossref","is-referenced-by-count":20,"title":["Robust Averaging of Covariances for EEG Recordings Classification in Motor Imagery Brain-Computer Interfaces"],"prefix":"10.1162","volume":"29","author":[{"given":"Takashi","family":"Uehara","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Sartori","sequence":"additional","affiliation":[{"name":"School of Information and Automation Engineering, Universit\u00e0 Politecnica delle Marche, Ancona 1-60131, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Toshihisa","family":"Tanaka","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, and RIKEN Brain Institute, Saitama 351-0198, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simone","family":"Fiori","sequence":"additional","affiliation":[{"name":"School of Information and Automation Engineering, Universit\u00e0 Politecnica delle Marche, Ancona 1-60131, Italy, and Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 Politecnica delle Marche, 1-60131, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.5626\/JCSE.2013.7.2.139"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1137\/050637996"},{"key":"B3","volume-title":"Statistics for management","author":"Arulmozhi G.","year":"2009"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2015.09.003"},{"key":"B5","first-page":"19","author":"Barachant A.","year":"2013","journal-title":"Proceedings of the TOBI Workshop IV"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2011.2172210"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2012.12.039"},{"key":"B8","first-page":"1869","volume-title":"Advances in neural information processing systems","author":"Bartz D.","year":"2013"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.11.028"},{"key":"B10","volume-title":"Positive definite matrices","author":"Bhatia R.","year":"2007"},{"key":"B11","volume-title":"Pattern recognition and machine learning","author":"Bishop C. 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