{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T12:11:31Z","timestamp":1770984691186,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T00:00:00Z","timestamp":1731974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Texas National Security Network Excellence Fund award for Environmental Sensing Security Sentinels","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}]},{"name":"Texas National Security Network Excellence Fund award for Environmental Sensing Security Sentinels","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}]},{"name":"Texas National Security Network Excellence Fund award for Environmental Sensing Security Sentinels","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}]},{"name":"SOFWERX award for Machine Learning for Robotic Teams","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}]},{"name":"SOFWERX award for Machine Learning for Robotic Teams","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}]},{"name":"SOFWERX award for Machine Learning for Robotic Teams","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}]},{"DOI":"10.13039\/100000001","name":"NSF Award","doi-asserted-by":"publisher","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF Award","doi-asserted-by":"publisher","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF Award","doi-asserted-by":"publisher","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Texas at Dallas Office of Sponsored Programs","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}]},{"name":"University of Texas at Dallas Office of Sponsored Programs","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}]},{"name":"University of Texas at Dallas Office of Sponsored Programs","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}]},{"name":"TRECIS CC* Cyberteam","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}]},{"name":"TRECIS CC* Cyberteam","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}]},{"name":"TRECIS CC* Cyberteam","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}]},{"DOI":"10.13039\/100013031","name":"EPA P3","doi-asserted-by":"publisher","award":["OAC-2115094"],"award-info":[{"award-number":["OAC-2115094"]}],"id":[{"id":"10.13039\/100013031","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013031","name":"EPA P3","doi-asserted-by":"publisher","award":["#2019135"],"award-info":[{"award-number":["#2019135"]}],"id":[{"id":"10.13039\/100013031","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013031","name":"EPA P3","doi-asserted-by":"publisher","award":["84057001-0"],"award-info":[{"award-number":["84057001-0"]}],"id":[{"id":"10.13039\/100013031","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>We introduce a new model for non-linear endmember extraction and spectral unmixing of hyperspectral imagery called Generative Simplex Mapping (GSM). The model represents endmember mixing using a latent space of points sampled within a (n\u22121)-simplex corresponding to n unique sources. Barycentric coordinates within this simplex are naturally interpreted as relative endmember abundances satisfying both the abundance sum-to-one and abundance non-negativity constraints. Points in this latent space are mapped to reflectance spectra via a flexible function combining linear and non-linear mixing. Due to the probabilistic formulation of the GSM, spectral variability is also estimated by a precision parameter describing the distribution of observed spectra. Model parameters are determined using a generalized expectation-maximization algorithm, which guarantees non-negativity for extracted endmembers. We first compare the GSM against three varieties of non-negative matrix factorization (NMF) on a synthetic data set of linearly mixed spectra from the USGS spectral database. Here, the GSM performed favorably for both endmember accuracy and abundance estimation with all non-linear contributions driven to zero by the fitting procedure. In a second experiment, we apply the GTM to model non-linear mixing in real hyperspectral imagery captured over a pond in North Texas. The model accurately identified spectral signatures corresponding to near-shore algae, water, and rhodamine tracer dye introduced into the pond to simulate water contamination by a localized source. Abundance maps generated using the GSM accurately track the evolution of the dye plume as it mixes into the surrounding water.<\/jats:p>","DOI":"10.3390\/rs16224316","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T07:51:15Z","timestamp":1732002675000},"page":"4316","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Generative Simplex Mapping: Non-Linear Endmember Extraction and Spectral Unmixing for Hyperspectral Imagery"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5910-0183","authenticated-orcid":false,"given":"John","family":"Waczak","sequence":"first","affiliation":[{"name":"Hanson Center for Space Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4265-9543","authenticated-orcid":false,"given":"David J.","family":"Lary","sequence":"additional","affiliation":[{"name":"Hanson Center for Space Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Loizzo, R., Guarini, R., Longo, F., Scopa, T., Formaro, R., Facchinetti, C., and Varacalli, G. 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