{"status":"public","_id":"40845","date_created":"2023-01-30T11:52:01Z","doi":"10.1109/MLSP.2010.5589225","user_id":"43497","author":[{"last_name":"Vía","full_name":"Vía, J.","first_name":"J."},{"full_name":"Ramírez, D.","last_name":"Ramírez","first_name":"D."},{"first_name":"I.","full_name":"Santamaría, I.","last_name":"Santamaría"},{"full_name":"Vielva, L.","last_name":"Vielva","first_name":"L."}],"year":"2010","citation":{"apa":"Vía, J., Ramírez, D., Santamaría, I., &#38; Vielva, L. (2010). Improperness Measures for Quaternion Random Vectors. <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">https://doi.org/10.1109/MLSP.2010.5589225</a>","chicago":"Vía, J., D. Ramírez, I. Santamaría, and L. Vielva. “Improperness Measures for Quaternion Random Vectors.” In <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> Finland, 2010. <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">https://doi.org/10.1109/MLSP.2010.5589225</a>.","mla":"Vía, J., et al. “Improperness Measures for Quaternion Random Vectors.” <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i>, 2010, doi:<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>.","ama":"Vía J, Ramírez D, Santamaría I, Vielva L. Improperness Measures for Quaternion Random Vectors. In: <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> ; 2010. doi:<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>","ieee":"J. Vía, D. Ramírez, I. Santamaría, and L. Vielva, “Improperness Measures for Quaternion Random Vectors,” 2010, doi: <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>.","bibtex":"@inproceedings{Vía_Ramírez_Santamaría_Vielva_2010, place={Finland}, title={Improperness Measures for Quaternion Random Vectors}, DOI={<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>}, booktitle={Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.}, author={Vía, J. and Ramírez, D. and Santamaría, I. and Vielva, L.}, year={2010} }","short":"J. Vía, D. Ramírez, I. Santamaría, L. Vielva, in: Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process., Finland, 2010."},"type":"conference","department":[{"_id":"263"}],"place":"Finland","date_updated":"2023-01-30T11:56:58Z","title":"Improperness Measures for Quaternion Random Vectors","abstract":[{"lang":"eng","text":"It has been recently proved that the two main kinds of quaternion improperness require two different kinds of widely linear process- ing. In this work, we show that these definitions satisfy some im- portant properties, which include the invariance to quaternion lin- ear transformations and right Clifford translations, as well as some clear connections with the case of proper complex vectors. More- over, we introduce a new kind of quaternion properness, which clearly relates the two previous definitions, and propose three mea- sures for the degree of improperness of a quaternion vector. The proposed measures are based on the Kullback-Leibler divergence between two zero-mean quaternion Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. These measures allow us to quan- tify the entropy loss due to the improperness of the quaternion vec- tor, and they admit an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented co- variance matrices."}],"publication":"Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process."}