{"id":"https://openalex.org/W17418856","doi":null,"title":"Maps for the Visualization of high-dimensional Data Spaces","display_name":"Maps for the Visualization of high-dimensional Data Spaces","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W17418856","mag":"17418856"},"language":"en","primary_location":{"id":"mag:17418856","doi":null,"is_oa":false,"landing_page_url":"https://www.researchgate.net/profile/Alfred_Ultsch/publication/228706090_Maps_for_the_visualization_of_high-dimensional_data_spaces/links/544652950cf2f14fb80f3134.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078097779","display_name":"Alfred Ultsch","orcid":"https://orcid.org/0000-0002-7845-3283","observed_orcids":["https://orcid.org/0000-0002-7845-3283"]},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alfred Ultsch","raw_affiliation_strings":["\u2002University of Marburg"],"raw_orcid":"https://orcid.org/0000-0002-7845-3283","affiliations":[{"raw_affiliation_string":"\u2002University of Marburg","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078097779"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":9.3662,"has_fulltext":true,"cited_by_count":196,"citation_normalized_percentile":{"value":0.98028114,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9413999915122986,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9413999915122986,"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/T10799","display_name":"Data Visualization and Analytics","score":0.04479999840259552,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.004999999888241291,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/u-matrix","display_name":"U-matrix","score":0.9430000185966492},{"id":"https://openalex.org/keywords/border-effects","display_name":"border effects","score":0.6019999980926514},{"id":"https://openalex.org/keywords/p-matrices","display_name":"P-matrices","score":0.7289999723434448},{"id":"https://openalex.org/keywords/high-dimensional-data-visualization","display_name":"high-dimensional data visualization","score":0.8809999823570251},{"id":"https://openalex.org/keywords/topology-preservation","display_name":"topology preservation","score":0.43299999833106995},{"id":"https://openalex.org/keywords/data-mining-visualization","display_name":"data mining visualization","score":0.5550000071525574}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6344369649887085},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6122080087661743},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5649638175964355},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5499448776245117},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.520638644695282},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.491629421710968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45738404989242554},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4413292109966278},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.43276864290237427},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.4210158884525299},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.387393593788147},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.32580268383026123},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3237079977989197},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32036951184272766},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31931039690971375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29304102063179016},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2797295153141022},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23526343703269958},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:17418856","doi":null,"is_oa":false,"landing_page_url":"https://www.researchgate.net/profile/Alfred_Ultsch/publication/228706090_Maps_for_the_visualization_of_high-dimensional_data_spaces/links/544652950cf2f14fb80f3134.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W65738273","https://openalex.org/W196843531","https://openalex.org/W1486234516","https://openalex.org/W1518498072","https://openalex.org/W1656697623","https://openalex.org/W1995875735","https://openalex.org/W2063218326","https://openalex.org/W2122705395","https://openalex.org/W2171029115"],"related_works":["https://openalex.org/W7096867040","https://openalex.org/W7097344105","https://openalex.org/W7100203470","https://openalex.org/W72235530","https://openalex.org/W3092603928","https://openalex.org/W4412877082","https://openalex.org/W2752665455","https://openalex.org/W2472434624","https://openalex.org/W7097790668","https://openalex.org/W1967156528"],"abstract_inverted_index":{"-The":[0],"U-Matrix":[1,20,67,74],"is":[2,27,92,110,166],"a":[3,41,48,60,93,120,124,154,158],"canonical":[4],"tool":[5],"for":[6,23,112,119,132,186],"the":[7,37,73,79,96,100,108,130,150,170,178],"display":[8,58,94,122,131,177],"of":[9,53,59,72,81,84,95,123,140,153,174],"distance":[10,151],"structures":[11],"in":[12,29,40,99],"data":[13,85,101,141,155,187],"space":[14,39,63,102,156,165],"using":[15,103],"emergent":[16],"SOM":[17],"(ESOM).":[18],"The":[19,87],"defined":[21,90],"originally":[22],"planar":[24,54,57,126],"map":[25,62],"spaces":[26],"extended":[28],"this":[30,76],"work":[31],"to":[32,144,169],"toroid":[33,61],"neuron":[34,38,127],"spaces.":[35,55],"Embedding":[36],"finite":[42],"but":[43],"borderless":[44,159],"space,":[45],"such":[46],"as":[47,89,157],"torus,":[49],"avoids":[50],"border":[51],"effects":[52],"A":[56],"disrupts,":[64],"however,":[65],"coherent":[66],"structures.":[68,180],"Tiling":[69],"multiple":[70,82],"instances":[71],"solves":[75],"problem":[77],"at":[78],"cost":[80],"images":[83,139],"points.":[86],"P-Matrix,":[88],"here,":[91],"density":[97,134,179],"relationships":[98],"Pareto":[104],"Density":[105],"Estimation.":[106],"While":[107],"P-Matrix":[109],"useful":[111],"clustering,":[113],"it":[114],"can":[115],"also":[116],"be":[117],"used":[118],"non-ambiguous":[121],"non":[125],"space.":[128],"Centering":[129],"high":[133],"regions":[135],"and":[136,146,189],"removing":[137],"ambiguous":[138],"points":[142],"leads":[143],"U-Maps":[145,148],"P-Maps.":[147],"depict":[149],"structure":[152],"three":[160],"dimensional":[161],"landscape":[162],"whose":[163],"floor":[164],"ordered":[167],"according":[168],"topology":[171],"preserving":[172],"features":[173],"ESOM.":[175],"P-Maps":[176],"Both":[181],"maps":[182],"are":[183],"specially":[184],"suited":[185],"mining":[188],"knowledge":[190],"discovery.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":15}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}