{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T08:03:52Z","timestamp":1776931432881,"version":"3.51.2"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T00:00:00Z","timestamp":1539820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Hyperspectral unmixing, which decomposes mixed pixels into endmembers and corresponding abundance maps of endmembers, has obtained much attention in recent decades. Most spectral unmixing algorithms based on non-negative matrix factorization (NMF) do not explore the intrinsic manifold structure of hyperspectral data space. Studies have proven image data is smooth along the intrinsic manifold structure. Thus, this paper explores the intrinsic manifold structure of hyperspectral data space and introduces manifold learning into NMF for spectral unmixing. Firstly, a novel projection equation is employed to model the intrinsic structure of hyperspectral image preserving spectral information and spatial information of hyperspectral image. Then, a graph regularizer which establishes a close link between hyperspectral image and abundance matrix is introduced in the proposed method to keep intrinsic structure invariant in spectral unmixing. In this way, decomposed abundance matrix is able to preserve the true abundance intrinsic structure, which leads to a more desired spectral unmixing performance. At last, the experimental results including the spectral angle distance and the root mean square error on synthetic and real hyperspectral data prove the superiority of the proposed method over the previous methods.<\/jats:p>","DOI":"10.3390\/s18103528","type":"journal-article","created":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T10:08:02Z","timestamp":1539943682000},"page":"3528","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Spectral Unmixing of Hyperspectral Remote Sensing Imagery via Preserving the Intrinsic Structure Invariant"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4870-7406","authenticated-orcid":false,"given":"Yang","family":"Shao","sequence":"first","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinhui","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuzhen","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinlin","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2244672","article-title":"Hyperspectral remote sensing data analysis and future challenge","volume":"1","author":"Plaza","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_2","first-page":"55","article-title":"A survey of spectral unmixing algorithms","volume":"14","author":"Keshava","year":"2003","journal-title":"Linc. Lab. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.1080\/09500340108235506","article-title":"Super-resolution technique of microzooming in electro-optical imaging systems","volume":"48","author":"Zhang","year":"2001","journal-title":"J. Mod. Opt."},{"key":"ref_4","first-page":"13","article-title":"Research progress on unmixing of hyperspectral remote sensing imagery","volume":"22","author":"Lan","year":"2018","journal-title":"J. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Winter, M.E. (1999, January 18\u201323). N-FINDR: An algorithm for fast autonomous spectral endmember determination in hyperspectral data. Proceedings of the SPIE\u2019s International Symposium on Optical Science, Engineering, and Instrumentation, Denver, CO, USA.","DOI":"10.1117\/12.366289"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TGRS.2005.844293","article-title":"Vertex component analysis: A fast algorithm to unmix hyperspectral data","volume":"43","author":"Nascimento","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2804","DOI":"10.1109\/TGRS.2006.881803","article-title":"A new growing method for simplex-based endmember extraction algorithm","volume":"44","author":"Chang","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/TGRS.2011.2158829","article-title":"A new maximum simplex volume method based on householder transformation for endmember extraction","volume":"50","author":"Liu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, J., and Bioucas-Dias, J. (2008, January 8\u201312). Minimum volume simplex analysis: A fast algorithm to unmix hyperspectral data. Proceedings of the IEEE Geoscience Remote Sensing Symposium (IGARSS\u201908), Boston, MA, USA.","DOI":"10.1109\/IGARSS.2008.4779330"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J. (2009, January 26\u201328). A variable splitting augmented Lagrangian approachto linear spectral unmixing. Proceedings of the 1st IEEE WHISPERS, Grenoble, France.","DOI":"10.1109\/WHISPERS.2009.5289072"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Nascimento, J., and Bioucas-Dias, J. (2007, January 23\u201328). Hyperspectral unmixing algorithm via dependent component analysis. Proceedings of the IEEE IGARSS, Barcelona, Spain.","DOI":"10.1109\/IGARSS.2007.4423734"},{"key":"ref_12","first-page":"556","article-title":"Algorithms for non-negative matrix factorization","volume":"Volume 13","author":"Lee","year":"2000","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4418","DOI":"10.1109\/TSP.2009.2025802","article-title":"A convex analysis based minimum-volume enclosing simplex algorithm for hyperspectral unmixing","volume":"57","author":"Chan","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.laa.2005.06.025","article-title":"Nonnegative matrix factorization for spectral data analysis","volume":"Volume 416","author":"Paura","year":"2006","journal-title":"Linear Algebra and Its Applications"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1109\/TGRS.2010.2068053","article-title":"An Approach Based on Constrained Nonnegative Matrix Factoriza-tion to unmix hyperspectral data","volume":"49","author":"Liu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/JSTARS.2013.2242255","article-title":"An endmember dissimilarity constrained non-negative matrix factorization method for hyperspectral unmixing","volume":"6","author":"Wang","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1109\/TIP.2010.2081678","article-title":"Blind spectral unmixing based on sparse nonnegative matrix factorization","volume":"20","author":"Yang","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1109\/TGRS.2006.888466","article-title":"Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization","volume":"45","author":"Miao","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2632","DOI":"10.1109\/JSTARS.2015.2427656","article-title":"Projection-based NMF for hyperspectral unmixing","volume":"8","author":"Yuan","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4282","DOI":"10.1109\/TGRS.2011.2144605","article-title":"Hyperspectral Unmixing via L1\/2 Sparsity-constrained Nonnegative Matrix Factorization","volume":"49","author":"Qian","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.isprsjprs.2013.11.014","article-title":"Structured sparse method for hyperspectral unmixing","volume":"88","author":"Zhu","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_22","unstructured":"Prasad, T., John, L., and Alfredo, H. (2001). Hyperspectral Remote Sensing of Vegetation, CRC Press."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chang, C.I. (2007). Hyperspectral Data Exploitation: Theory and Applications, John Wiley & Sons Inc.","DOI":"10.1002\/0470124628"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lee, J.M. (2002). Introduction to Smooth Manifolds, Springer.","DOI":"10.1007\/978-0-387-21752-9"},{"key":"ref_25","first-page":"585","article-title":"Laplacian eigenmaps and spectral techniques for embedding and clustering","volume":"14","author":"Belkin","year":"2001","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TGRS.2004.842292","article-title":"Exploiting manifold geometry in hyperspectral imagery","volume":"43","author":"Bachmann","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1109\/LGRS.2011.2107877","article-title":"Region-based spatial preprocessing for endmember extraction and spectral unmixing","volume":"8","author":"Martin","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1109\/JSTARS.2012.2199282","article-title":"Enhancing spectral unmixing by local neighborhood weights","volume":"5","author":"Liu","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4565","DOI":"10.1109\/TIP.2016.2590324","article-title":"Hyperspectral unmixing in presence of endmember variability, nonlinearity, or mismodeling effects","volume":"25","author":"Halimi","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zou, J., Lan, J., and Shao, Y. (2018). A hierarchical sparsity unmixing method to address endmember variability in hyperspectral image. Remote Sens., 10.","DOI":"10.3390\/rs10050738"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1049\/el:20060983","article-title":"Multilayer nonnegative matrix factorization","volume":"42","author":"Cichocki","year":"2006","journal-title":"Electron. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.rse.2006.01.006","article-title":"Estimation of yellow starthistle abundance through CASI-2 hyperspectral imagery using linear spectral mixture models","volume":"101","author":"Miao","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/02757259609532303","article-title":"A review of mixture modeling techniques for sub-pixel land cover estimation","volume":"13","author":"Karnieli","year":"1996","journal-title":"Remote Sens. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/79.974727","article-title":"Spectral unmixing","volume":"19","author":"Keshava","year":"2002","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"234","DOI":"10.2307\/143141","article-title":"A computer movie simulating urban growth in the Detroit region","volume":"46","author":"Tobler","year":"1970","journal-title":"Econ. Geogr."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2679","DOI":"10.1109\/TGRS.2009.2014945","article-title":"Spatial preprocessing for endmember extraction","volume":"47","author":"Zortea","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","unstructured":"(2018, September 22). USGS, Available online: https:\/\/speclab.cr.usgs.gov\/spectral-lib.html."},{"key":"ref_38","unstructured":"(2015, November 27). Opticks. Available online: http:\/\/opticks.org\/confluence\/display\/opticks\/Sample+Data."},{"key":"ref_39","unstructured":"Zhu, F.Y. (2018, September 21). Hyperspectral Unmixing Datasets & Ground Truths. Available online: http:\/\/www.escience.cn\/people\/feiyunZHU\/Dataset_GT.html."},{"key":"ref_40","unstructured":"(2018, September 20). SpecLab, Available online: http:\/\/speclab.cr.usgs.gov\/cuprite.html."},{"key":"ref_41","unstructured":"Swayze, G., Clark, R., Sutley, S., and Gallagher, A. (1992, January 1\u20135). Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada. Proceedings of the 3rd Annual JPL Airborne Geoscience Workshop, Pasadena, CA, USA."},{"key":"ref_42","unstructured":"Swayze, G.A. (1997). The Hydrothermal and Structural History of the Cuprite Mining District, Southwestern Nevada: An Integrated Geological and Geophysical Approach, Stanford University."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1109\/TGRS.2003.819189","article-title":"Estimation of number of spectrally distinct signal sources in hyperspectral imagery","volume":"42","author":"Chang","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","first-page":"1457","article-title":"Non-negative matrix factorization with sparseness constraints","volume":"5","author":"Hoyer","year":"2004","journal-title":"J. Mach. Learn. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3528\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:36Z","timestamp":1760196396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3528"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,18]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103528"],"URL":"https:\/\/doi.org\/10.3390\/s18103528","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,18]]}}}