{"id":"https://openalex.org/W2760901445","doi":"https://doi.org/10.1109/tip.2018.2795744","title":"A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing","display_name":"A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing","publication_year":2018,"publication_date":"2018-01-19","ids":{"openalex":"https://openalex.org/W2760901445","doi":"https://doi.org/10.1109/tip.2018.2795744","mag":"2760901445","pmid":"https://pubmed.ncbi.nlm.nih.gov/29432104"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2018.2795744","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2018.2795744","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.00075","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yuan Zhou","orcid":"https://orcid.org/0000-0002-7846-8629"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuan Zhou","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Anand Rangarajan","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anand Rangarajan","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":null,"display_name":"Paul D. Gader","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul D. Gader","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":10.8474,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.98452313,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"27","issue":"5","first_page":"2242","last_page":"2256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.007499999832361937,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/endmember","display_name":"Endmember","score":0.9642000198364258},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.8374999761581421},{"id":"https://openalex.org/keywords/hyperspectral-imaging","display_name":"Hyperspectral imaging","score":0.7907000184059143},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6769000291824341},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.5633999705314636},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5034000277519226},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4708000123500824},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.46709999442100525},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4481000006198883},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.41769999265670776}],"concepts":[{"id":"https://openalex.org/C58237817","wikidata":"https://www.wikidata.org/wiki/Q5376204","display_name":"Endmember","level":3,"score":0.9642000198364258},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.8374999761581421},{"id":"https://openalex.org/C159078339","wikidata":"https://www.wikidata.org/wiki/Q959005","display_name":"Hyperspectral imaging","level":2,"score":0.7907000184059143},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6769000291824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6348000168800354},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5654000043869019},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5034000277519226},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4481000006198883},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.41769999265670776},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.3840000033378601},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3571000099182129},{"id":"https://openalex.org/C56672385","wikidata":"https://www.wikidata.org/wiki/Q17157111","display_name":"Mixture distribution","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.33410000801086426},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.32109999656677246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3167000114917755},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2985999882221222},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.2745000123977661},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2018.2795744","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2018.2795744","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:29432104","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29432104","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:arXiv.org:1710.00075","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.00075","pdf_url":"https://arxiv.org/pdf/1710.00075","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.00075","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.00075","pdf_url":"https://arxiv.org/pdf/1710.00075","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1524571335","https://openalex.org/W1570876803","https://openalex.org/W1571413698","https://openalex.org/W1574816920","https://openalex.org/W1940108662","https://openalex.org/W1952261593","https://openalex.org/W1963659868","https://openalex.org/W1965340435","https://openalex.org/W1967639437","https://openalex.org/W1972293418","https://openalex.org/W1990231296","https://openalex.org/W1991900070","https://openalex.org/W2014374676","https://openalex.org/W2016201611","https://openalex.org/W2037328426","https://openalex.org/W2042626896","https://openalex.org/W2048858906","https://openalex.org/W2051358843","https://openalex.org/W2069921544","https://openalex.org/W2074342013","https://openalex.org/W2074550148","https://openalex.org/W2076123399","https://openalex.org/W2076332129","https://openalex.org/W2078222544","https://openalex.org/W2087964169","https://openalex.org/W2091397530","https://openalex.org/W2097211423","https://openalex.org/W2098149888","https://openalex.org/W2107219953","https://openalex.org/W2109115094","https://openalex.org/W2110096996","https://openalex.org/W2122976738","https://openalex.org/W2124781164","https://openalex.org/W2127523161","https://openalex.org/W2136134691","https://openalex.org/W2139047226","https://openalex.org/W2139766511","https://openalex.org/W2143457518","https://openalex.org/W2144719328","https://openalex.org/W2144881411","https://openalex.org/W2145035344","https://openalex.org/W2157321686","https://openalex.org/W2163886442","https://openalex.org/W2239643428","https://openalex.org/W2247723941","https://openalex.org/W2326057689","https://openalex.org/W2542152021","https://openalex.org/W2608860984","https://openalex.org/W4233760599","https://openalex.org/W4248081355","https://openalex.org/W4392677642"],"related_works":[],"abstract_inverted_index":{"Hyperspectral":[0],"unmixing":[1],"while":[2],"considering":[3],"endmember":[4,53,189],"variability":[5],"is":[6,38,74,80],"usually":[7],"performed":[8],"by":[9,209],"the":[10,15,33,58,63,66,70,100,103,116,118,147,150,161,169,180,187,196],"normal":[11],"compositional":[12],"model,":[13],"where":[14],"endmembers":[16,148,162],"for":[17,160,191],"each":[18,164,192],"pixel":[19,68],"are":[20],"assumed":[21],"to":[22,51,123,158,168,212],"be":[23,134],"sampled":[24],"from":[25,82,89,144],"unimodal":[26],"Gaussian":[27,47],"distributions.":[28],"However,":[29],"in":[30,149],"real":[31,203],"applications,":[32],"distribution":[34,64,171,183],"of":[35,65,99],"a":[36,76,95,124,127,156],"material":[37],"often":[39],"not":[40,177],"Gaussian.":[41],"In":[42],"this":[43,79],"paper,":[44],"we":[45],"use":[46],"mixture":[48],"models":[49],"(GMM)":[50],"represent":[52],"variability.":[54],"We":[55,194],"show,":[56],"given":[57,102],"GMM":[59,77,106,198],"starting":[60],"premise,":[61],"that":[62],"mixed":[67],"(under":[69],"linear":[71],"mixing":[72],"model)":[73],"also":[75,186],"(and":[78],"shown":[81],"two":[83],"perspectives).":[84],"The":[85,140],"first":[86],"perspective":[87,142],"originates":[88,143],"random":[90],"variable":[91],"transformations":[92],"and":[93,105,111,182,202,205],"gives":[94],"conditional":[96,119],"density":[97,120],"function":[98,121],"pixels":[101],"abundances":[104,181],"parameters.":[107],"With":[108],"proper":[109],"smoothness":[110],"sparsity":[112],"prior":[113],"constraints":[114],"on":[115,199],"abundances,":[117],"leads":[122],"standard":[125],"maximum":[126],"posteriori":[128],"(MAP":[129],")":[130],"problem":[131],"which":[132,152],"can":[133,176],"solved":[135],"using":[136],"generalized":[137],"expectation":[138],"maximization.":[139],"second":[141],"marginalizing":[145],"over":[146],"GMM,":[151],"provides":[153],"us":[154],"with":[155],"foundation":[157],"solve":[159],"at":[163],"pixel.":[165,193],"Hence,":[166],"compared":[167],"other":[170],"based":[172],"methods,":[173],"our":[174],"model":[175],"only":[178],"estimate":[179],"parameters,":[184],"but":[185],"distinct":[188],"set":[190],"tested":[195],"proposed":[197],"several":[200],"synthetic":[201],"datasets,":[204],"showed":[206],"its":[207],"potential":[208],"comparing":[210],"it":[211],"current":[213],"popular":[214],"methods.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":3}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2017-10-20T00:00:00"}