{"id":"https://openalex.org/W4413311389","doi":"https://doi.org/10.3390/e27080875","title":"Autoencoder-like Sparse Non-Negative Matrix Factorization with Structure Relationship Preservation","display_name":"Autoencoder-like Sparse Non-Negative Matrix Factorization with Structure Relationship Preservation","publication_year":2025,"publication_date":"2025-08-19","ids":{"openalex":"https://openalex.org/W4413311389","doi":"https://doi.org/10.3390/e27080875","pmid":"https://pubmed.ncbi.nlm.nih.gov/40870347"},"language":"en","primary_location":{"id":"doi:10.3390/e27080875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27080875","pdf_url":"https://www.mdpi.com/1099-4300/27/8/875/pdf?version=1755608044","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/8/875/pdf?version=1755608044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048752310","display_name":"Ling Zhong","orcid":"https://orcid.org/0000-0001-6604-2068"},"institutions":[{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Zhong","raw_affiliation_strings":["School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041809431","display_name":"Haiyan Gao","orcid":"https://orcid.org/0000-0002-5736-0600"},"institutions":[{"id":"https://openalex.org/I4210088494","display_name":"Gansu Province Computing Center","ror":"https://ror.org/003wq4h14","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210088494"]},{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haiyan Gao","raw_affiliation_strings":["Key Laboratory of Digital Economy and Social Computing Science of Gansu, Lanzhou 730020, China","School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"],"raw_orcid":"https://orcid.org/0000-0002-5736-0600","affiliations":[{"raw_affiliation_string":"Key Laboratory of Digital Economy and Social Computing Science of Gansu, Lanzhou 730020, China","institution_ids":["https://openalex.org/I4210088494"]},{"raw_affiliation_string":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China","institution_ids":["https://openalex.org/I4210152533"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041809431"],"corresponding_institution_ids":["https://openalex.org/I4210088494","https://openalex.org/I4210152533"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17540315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"8","first_page":"875","last_page":"875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9801999926567078,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.6984614133834839},{"id":"https://openalex.org/keywords/autoencoder","display_name":"Autoencoder","score":0.6187955141067505},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6018965840339661},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5996564030647278},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.5682237148284912},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5354663729667664},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5040368437767029},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.4781961441040039},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.46170762181282043},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.42786169052124023},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4265488088130951},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41404736042022705},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.41381603479385376},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3516351878643036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3436056077480316},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12640008330345154},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.10831716656684875},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.09585332870483398}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6984614133834839},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.6187955141067505},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6018965840339661},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5996564030647278},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.5682237148284912},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5354663729667664},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5040368437767029},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.4781961441040039},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.46170762181282043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42786169052124023},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4265488088130951},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41404736042022705},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.41381603479385376},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3516351878643036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3436056077480316},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12640008330345154},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.10831716656684875},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.09585332870483398},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27080875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27080875","pdf_url":"https://www.mdpi.com/1099-4300/27/8/875/pdf?version=1755608044","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40870347","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40870347","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:216ecadc8a394458ba1213e4d78e8bfc","is_oa":true,"landing_page_url":"https://doaj.org/article/216ecadc8a394458ba1213e4d78e8bfc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 8, p 875 (2025)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:11193384","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12385698","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27080875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27080875","pdf_url":"https://www.mdpi.com/1099-4300/27/8/875/pdf?version=1755608044","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1011403018","display_name":null,"funder_award_id":"23JRRA1186","funder_id":"https://openalex.org/F4320322880","funder_display_name":"Natural Science Foundation of Gansu Province"}],"funders":[{"id":"https://openalex.org/F4320322880","display_name":"Natural Science Foundation of Gansu Province","ror":null},{"id":"https://openalex.org/F4320327557","display_name":"National Office for Philosophy and Social Sciences","ror":"https://ror.org/04m0ms912"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413311389.pdf","grobid_xml":"https://content.openalex.org/works/W4413311389.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1902027874","https://openalex.org/W2002469984","https://openalex.org/W2036285176","https://openalex.org/W2043545458","https://openalex.org/W2059713011","https://openalex.org/W2063069198","https://openalex.org/W2089468765","https://openalex.org/W2100068253","https://openalex.org/W2108119513","https://openalex.org/W2177066871","https://openalex.org/W2494395359","https://openalex.org/W2746043465","https://openalex.org/W2767834929","https://openalex.org/W2776766374","https://openalex.org/W2793733641","https://openalex.org/W2993529567","https://openalex.org/W3041063529","https://openalex.org/W3120396023","https://openalex.org/W3137047567","https://openalex.org/W3152682768","https://openalex.org/W4220965490","https://openalex.org/W4224757231","https://openalex.org/W4225496219","https://openalex.org/W4226514587","https://openalex.org/W4306928527","https://openalex.org/W4387517617","https://openalex.org/W4387535095","https://openalex.org/W4392973078","https://openalex.org/W4393166997","https://openalex.org/W4401630077","https://openalex.org/W4404415401","https://openalex.org/W4404650442","https://openalex.org/W4404918237","https://openalex.org/W4407080802","https://openalex.org/W4409328281","https://openalex.org/W4409371212","https://openalex.org/W4411232189","https://openalex.org/W6665037457","https://openalex.org/W6675747103","https://openalex.org/W6676321539","https://openalex.org/W6677759377","https://openalex.org/W6680012447","https://openalex.org/W6683799998","https://openalex.org/W6720006811","https://openalex.org/W6780216468"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840"],"abstract_inverted_index":{"Clustering":[0],"algorithms":[1],"based":[2],"on":[3,58,148,160],"non-negative":[4,48],"matrix":[5,49,66,151],"factorization":[6,50,67,74],"(NMF)":[7],"have":[8],"garnered":[9],"significant":[10],"attention":[11],"in":[12],"data":[13,37,105],"mining":[14],"due":[15],"to":[16,28,71,91,113,125],"their":[17],"strong":[18],"interpretability":[19],"and":[20,31,76,119,133,142],"computational":[21],"simplicity.":[22],"However,":[23],"traditional":[24],"NMF":[25],"often":[26],"struggles":[27],"effectively":[29],"capture":[30,92],"preserve":[32],"topological":[33,100],"structure":[34,52,101],"information":[35,102],"between":[36,96,130,140],"during":[38],"low-dimensional":[39,131],"representation.":[40],"Therefore,":[41],"this":[42],"paper":[43],"proposes":[44],"an":[45,107],"autoencoder-like":[46],"sparse":[47,144],"with":[51],"relationship":[53],"preservation":[54],"(ASNMF-SRP).":[55],"Firstly,":[56],"drawing":[57],"the":[59,73,80,104,115,121,127,134,149,153],"principle":[60],"of":[61,79,103,117],"autoencoders,":[62],"a":[63,84,143],"\"decoder-encoder\"":[64],"co-optimization":[65],"framework":[68],"is":[69,89,123,146],"constructed":[70],"enhance":[72],"stability":[75],"representation":[77],"capability":[78],"coefficient":[81,150],"matrix.":[82],"Then,":[83],"preference-adjusted":[85],"random":[86],"walk":[87],"strategy":[88],"introduced":[90],"higher-order":[93],"neighborhood":[94],"relationships":[95,139],"samples,":[97],"encoding":[98],"multi-order":[99],"through":[106],"optimal":[108],"graph":[109],"regularization":[110],"term.":[111],"Simultaneously,":[112],"mitigate":[114],"impact":[116],"noise":[118],"outliers,":[120],"l2,1-norm":[122],"used":[124],"constrain":[126],"feature":[128,138],"correlation":[129],"representations":[132],"original":[135],"data,":[136,141],"preserving":[137],"constraint":[145],"imposed":[147],"via":[152],"inner":[154],"product.":[155],"Finally,":[156],"clustering":[157,170],"experiments":[158],"conducted":[159],"8":[161],"public":[162],"datasets":[163],"demonstrate":[164],"that":[165],"ASNMF-SRP":[166],"consistently":[167],"exhibits":[168],"favorable":[169],"performance.":[171]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}