{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:18:01Z","timestamp":1777443481552,"version":"3.51.4"},"reference-count":39,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T00:00:00Z","timestamp":1765929600000},"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":[[2026,4]]},"abstract":"<jats:p>\n                    Complex-valued chemometrics utilizes both the absorption index and refractive index spectra. Through application of a Kramers\u2013Kronig transformation, it can also be extended to absorbance and Raman spectra. In this work, we expand complex-valued chemometrics to include partial least squares (PLS) regression. Several strategies for implementing complex-valued PLS are explored. One approach builds on the nonlinear iterative partial least squares (NIPALS) formalism to compute real and imaginary components of the PLS solutions in parallel. Additionally, as both the real and imaginary parts can assume positive or negative values, this results in 2\n                    <jats:italic toggle=\"yes\">\n                      <jats:sup>N<\/jats:sup>\n                    <\/jats:italic>\n                    possible solutions for\n                    <jats:italic toggle=\"yes\">N<\/jats:italic>\n                    components. In this case, the optimal solutions are selected using a brute-force approach combined with a nested leave-one-out (LOO) scheme. Additionally, single-value decomposition (SVD) can be directly applied to the complex matrix product of the spectral and concentration matrices. We compare these approaches using complex refractive index spectra of mixtures from the thermodynamically ideal systems benzene\u2013toluene, benzene\u2013cyclohexane, and benzene\u2013carbon tetrachloride (CCl\n                    <jats:sub>4<\/jats:sub>\n                    ). In particular, when the high-wavenumber refractive index differs between the neat components, complex-valued PLS achieves errors more than an order of magnitude lower than conventional PLS based solely on the imaginary part.\n                  <\/jats:p>","DOI":"10.1177\/00037028251401941","type":"journal-article","created":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T11:51:07Z","timestamp":1763466667000},"page":"416-427","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Complex-Valued Chemometrics in Spectroscopy: Partial Least Squares Regression"],"prefix":"10.1177","volume":"80","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)"},{"name":"Friedrich Schiller University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrii","family":"Kutsyk","sequence":"additional","affiliation":[{"name":"Lightnovo ApS, Blokken 11, Birker\u00f8d, 3460 Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4257-593X","authenticated-orcid":false,"given":"Juergen","family":"Popp","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT)"},{"name":"Friedrich Schiller University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2025,12,17]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780203909805"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/C2020-0-01907-9"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-64144-2"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1021\/ac00162a020"},{"key":"e_1_3_3_6_2","author":"Mayerh\u00f6fer T.G.","year":"2024","unstructured":"Mayerh\u00f6fer T.G.. 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