{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T03:05:15Z","timestamp":1783652715426,"version":"3.55.0"},"reference-count":40,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2025,5,25]],"date-time":"2025-05-25T00:00:00Z","timestamp":1748131200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Appl Spectrosc"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>\n                    We present the first implementation of complex-valued classical least squares (CLS) regression in spectroscopy. Although the results indicate that complex-valued CLS does not outperform methods that utilize only the more suitable part of the complex refractive index spectra, it includes an error detection feature that enables a self-correction mechanism. This mechanism decreases the mean absolute error (MAE) to approximately 26% relative to using only the mid-infrared (MIR) absorption index (\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    ) spectra for CLS, and to about 46% relative to using only the MIR refractive index (\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    ) spectra of benzene\u2013toluene mixtures. For benzene\u2013cyclohexane mixtures, the MAE was reduced to approximately 75% relative to the\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    spectra and 58% relative to the\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    spectra. In contrast, for benzene\u2013carbon tetrachloride (CCl\n                    <jats:sub>4<\/jats:sub>\n                    ) mixtures, i.e., a system that exhibits particularly large deviations from Beer\u2019s law, no improvement over the\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    spectra was observed; the\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    -based MAE was 81% relative to the\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    spectra. These percentages may further vary based on the complexity of the system, the spectral regions selected for CLS and the corresponding deviations from Beer\u2019s approximation.\n                  <\/jats:p>","DOI":"10.1177\/00037028251343908","type":"journal-article","created":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T01:51:27Z","timestamp":1748224287000},"page":"1768-1775","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Complex-Valued Chemometrics in Spectroscopy: Classical Least Squares Regression"],"prefix":"10.1177","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9396-7365","authenticated-orcid":false,"given":"Thomas G.","family":"Mayerh\u00f6fer","sequence":"first","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Str. 9, 07745 Jena, Germany"},{"name":"Institute of Physical Chemistry and Abbe Center of Photonics, Friedrich Schiller University, Helmholtzweg 4, 07743 Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oleksii","family":"Ilchenko","sequence":"additional","affiliation":[{"name":"The Danish National Research Foundation and Villum Foundation's Center for Intelligent Drug Delivery and Sensing Using Microcontainers and Nanomechanics (IDUN), Department of Health Technology, Technical University of Denmark, \u00d8rsteds Plads Building 345C, Kgs. Lyngby, 2800 Denmark"},{"name":"Lightnovo ApS, Blokken 11, Birker\u00f8d, 3460 Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrii","family":"Kutsyk","sequence":"additional","affiliation":[{"name":"Lightnovo ApS, Blokken 11, Birker\u00f8d, 3460 Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4257-593X","authenticated-orcid":false,"given":"J\u00fcrgen","family":"Pop","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Str. 9, 07745 Jena, Germany"},{"name":"Institute of Physical Chemistry and Abbe Center of Photonics, Friedrich Schiller University, Helmholtzweg 4, 07743 Jena, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,5,25]]},"reference":[{"key":"e_1_3_3_2_2","volume-title":"Data Analysis Using the Method of Least Squares: Extracting the Most Information from Experiments","author":"Wolberg J.R.","year":"2006","unstructured":"Wolberg J.R.. 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