{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T00:10:34Z","timestamp":1772064634541,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:00:00Z","timestamp":1556755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Limited to the low spatial resolution of the hyperspectral imaging sensor, mixed pixels are inevitable in hyperspectral images. Therefore, to obtain the endmembers and corresponding fractions in mixed pixels, hyperspectral unmixing becomes a hot spot in the field of remote sensing. Endmember spectral variability (ESV), which is common in hyperspectral images, affects spectral unmixing accuracy. This paper proposes a spectral unmixing method based on maximum margin criterion and derivative weights (MDWSU) to reduce the effect of ESV on spectral unmixing. Firstly, in the MDWSU model, an effective and fast algorithm is employed for establishing the endmember spectral library. Then a spectral weighting matrix based on the maximum margin criterion is constructed based on the endmember spectral library. Besides, derivative analysis and local neighborhood weights are merged into local neighborhood derivative weights, which act as a regularization term to penalize different abundance vectors. Local neighborhood derivative weights and spectral weighting matrix are proved to reduce the effect of ESV. Real hyperspectral data experiments show that the MDWSU model can obtain more accurate endmembers and abundance estimation. In addition, the experimental results, including the spectral angle distance and the root mean square error, prove the superiority of the MDWSU model over the previous methods.<\/jats:p>","DOI":"10.3390\/rs11091045","type":"journal-article","created":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T03:15:46Z","timestamp":1557198946000},"page":"1045","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Spectral Unmixing Method by Maximum Margin Criterion and Derivative Weights to Address Spectral Variability in Hyperspectral Imagery"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4870-7406","authenticated-orcid":false,"given":"Yang","family":"Shao","sequence":"first","affiliation":[{"name":"Department of Instrument Science and Technology, School of Automation and Electrical Engineering, University of Science and Technology, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinhui","family":"Lan","sequence":"additional","affiliation":[{"name":"Department of Instrument Science and Technology, School of Automation and Electrical Engineering, University of Science and Technology, Beijing 100083, China"},{"name":"Beijing Engineering Research Center of Industrial Spectrum Imaging, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,2]]},"reference":[{"key":"ref_1","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_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","unstructured":"Zou, J., and Lan, J. (2019). A multiscale hierarchical model for sparse hyperspectral unmixing. Remote Sens., 11.","DOI":"10.3390\/rs11050500"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/j.rse.2011.03.003","article-title":"Endmember variability in spectral mixture analysis: A review","volume":"115","author":"Somers","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/MSP.2013.2279177","article-title":"Endmember variability in hyperspectral analysis: Addressing spectral variability during spectral unmixing","volume":"31","author":"Zare","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ghaffari, O., Zoej, M.J.V., and Mokhtarzade, M. (2017). Reducing the effect of the endmembers\u2019 spectral variability by selecting the optimal spectral bands. Remote Sens., 9.","DOI":"10.3390\/rs9090884"},{"key":"ref_8","unstructured":"Costanzo, D.J. (2000, January 24\u201328). Hyperspectral imaging spectral variability experiment results. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Honolulu, HI, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3890","DOI":"10.1109\/TIP.2016.2579259","article-title":"Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability","volume":"25","author":"Drumetz","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.rse.2006.06.010","article-title":"Intra- and inter-class spectral variability of tropical tree species at La Selva, Costa Rica: Implications for species identification using HYDICE imagery","volume":"105","author":"Zhang","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0034-4257(98)00037-6","article-title":"Mapping chaparral in the santa monica mountains using multiple endmember spectral mixture models","volume":"65","author":"Roberts","year":"1998","journal-title":"Remote Sens Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1016\/j.rse.2009.03.018","article-title":"Hierarchical multiple endmember spectral mixture analysis (MESMA) of hyperspectral imagery for urban environments","volume":"113","author":"Franke","year":"2009","journal-title":"Remote Sens Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.rse.2006.09.005","article-title":"Sub-pixel mapping of urban land cover using multiple endmember spectral mixture analysis: Manaus, Brazil","volume":"106","author":"Powell","year":"2007","journal-title":"Remote Sens Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1109\/JSTARS.2011.2181340","article-title":"Automated extraction of image-based endmember bundles for improved spectral unmixing","volume":"5","author":"Somers","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Veganzones, M.A., Drumetz, L., Tochon, G., Mura, M.D., Plaza, A., Bioucas-Dias, J.-M., and Chanussot, J. (2014, January 24\u201327). A new extended linear mixing model to address spectral variability. Proceedings of the 6th IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Lausanne, Switzerland.","DOI":"10.1109\/WHISPERS.2014.8077595"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1109\/TGRS.2006.864389","article-title":"Constrained band selection for hyperspectral imagery","volume":"44","author":"Chang","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1109\/LGRS.2006.878240","article-title":"Band selection for hyperspectral image classification using mutual information","volume":"3","author":"Guo","year":"2006","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","first-page":"270","article-title":"Spectral mixture analysis to monitor defoliation in mixed-aged Eucalyptus globulus Labill plantations in southern Australia using Landsat 5-TM and EO-1 Hyperion data","volume":"12","author":"Somers","year":"2010","journal-title":"Int. J. Appl. Earth Obs."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3630","DOI":"10.1109\/TGRS.2009.2024207","article-title":"Magnitude- and shape-related feature integration in hyperspectral mixture analysis to monitor weeds in Citrus Orchards","volume":"47","author":"Asner","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1109\/TIM.2004.834070","article-title":"PCA-based feature selection scheme for machine defect classification","volume":"53","author":"Mahhi","year":"2004","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TGRS.2003.822750","article-title":"Wavelet-based feature extraction for improved endmember abundance estimation in linear unmixing of hyperspectral signals","volume":"42","author":"Li","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1934","DOI":"10.1109\/TGRS.2004.832239","article-title":"Derivative spectral unmixing of hyperspectral data applied to mixtures of lichen and rock","volume":"42","author":"Zhang","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0034-4257(00)00126-7","article-title":"A biogeophysical approach for automated SWIR unmixing of soils and vegetation","volume":"74","author":"Asner","year":"2000","journal-title":"Remote Sens. Environ."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1109\/LGRS.2010.2046134","article-title":"A Novel Approach Based on Fisher Discriminant Null Space for Decomposition of Mixed Pixels in Hyperspectral Imagery","volume":"7","author":"Jin","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","unstructured":"Boardman, J.W., Kruse, F.A., and Green, R.O. (1995, January 9\u201314). Mapping Target Signatures via Partial Unmixing of AVIRIS Data. Proceedings of the 5th Annual JPL Airborne Earth Science Workshop, Pasadena, CA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/TNN.2005.860852","article-title":"Efficient and Robust Feature Extraction by Maximum Margin Criterion","volume":"17","author":"Li","year":"2006","journal-title":"IEEE Trans. Neural Netw."},{"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":"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_30","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_31","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_32","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_33","doi-asserted-by":"crossref","unstructured":"Neville, R.A., Staenz, K., Szeredi, T., Lefebvre, J., and Hauff, P. (1999, January 21\u201324). Automatic endmember extraction from hyperspectral data for mineral exploration. Proceedings of the International Airborne Remote Sensing Conference and Exhibition, 4th\/21st Canadian Symposium on Remote Sensing, Ottawa, ON, Canada.","DOI":"10.4095\/219526"},{"key":"ref_34","unstructured":"(2015, November 27). Opticks. Available online: http:\/\/opticks.org\/confluence\/display\/opticks\/Sample+Data."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1109\/TGRS.2005.861408","article-title":"Weighted abundance-constrained linear spectral mixture analysis","volume":"44","author":"Chang","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1109\/36.992805","article-title":"A derivative-aided hyperspectral image analysis system for land-cover classification","volume":"40","author":"Tsai","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0034-4257(98)00032-7","article-title":"Derivative analysis of hyperspectral data","volume":"66","author":"Tsai","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0034-4257(92)90127-6","article-title":"Derivative reflectance spectroscopy to estimate suspended sediment concentration","volume":"40","author":"Chen","year":"1992","journal-title":"Remote Sens. Environ."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1021\/ac60214a047","article-title":"Smoothing and differentiation of data by simplified least squares procedures","volume":"7","author":"Savitzky","year":"1964","journal-title":"Anal. Chem."},{"key":"ref_40","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_41","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_42","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_43","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_44","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1109\/TGRS.2012.2213825","article-title":"Manifold Regularized Sparse NMF for Hyperspectral Unmixing","volume":"51","author":"Lu","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_45","first-page":"1457","article-title":"Non-negative matrix factorization with sparseness constraints","volume":"5","author":"Hoyer","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.5194\/gmd-7-1247-2014","article-title":"Root mean square error (RMSE) or mean absolute error (MAE)?\u2014Arguments against avoiding RMSE in the literature","volume":"7","author":"Chai","year":"2014","journal-title":"Geosci. Model Dev."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/36.911111","article-title":"Fully constrained least squares linear mixture analysis for material quantification in hyperspectral imagery","volume":"39","author":"Heinz","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_48","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":"Zhou","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_49","unstructured":"(2018, September 20). SpecLab, Available online: http:\/\/speclab.cr.usgs.gov\/cuprite.html."},{"key":"ref_50","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_51","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_52","unstructured":"(2019, January 17). USGS, Available online: https:\/\/speclab.cr.usgs.gov\/spectral-lib.html."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"6076","DOI":"10.1109\/TGRS.2016.2580702","article-title":"Robust Collaborative Nonnegative Matrix Factorization for Hyperspectral Unmixing","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_54","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_55","doi-asserted-by":"crossref","unstructured":"Revel, C., Deville, Y., Achrad, V., Briottet, X., and Weber, C. (2017). Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: A Hyperspectral Unmixing Method Dealing with Intra-Class Variability. Remote Sens., 10.","DOI":"10.3390\/rs10111706"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/36.841987","article-title":"Endmember Bundles: A New Approach to Incorporating Endmember Variability into Spectral Mixture Analysis","volume":"38","author":"Bateson","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_57","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_58","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_59","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J. (2009, January 26\u201328). A variable splitting augmented Lagrangian approach to linear spectral unmixing. Proceedings of the 1st IEEE WHISPERS, Grenoble, France.","DOI":"10.1109\/WHISPERS.2009.5289072"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Liu, L., Du, B., and Zhang, L. (2016). Hyperspectral Unmixing via Double Abundance Characteristics Constraints Based NMF. Remote Sens., 8.","DOI":"10.3390\/rs8060464"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Shao, Y., Lan, J., Zhang, Y., and Zou, J. (2018). Spectral Unmixing of Hyperspectral Remote Sensing Imagery via Preserving the Intrinsic Structure Invariant. Sensors, 18.","DOI":"10.3390\/s18103528"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.rse.2016.02.019","article-title":"Fractional vegetation cover estimation algorithm for Chinese GF-1 wide field view data","volume":"177","author":"Jia","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_63","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"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/9\/1045\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:48:49Z","timestamp":1760186929000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/9\/1045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,2]]},"references-count":63,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["rs11091045"],"URL":"https:\/\/doi.org\/10.3390\/rs11091045","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,2]]}}}