{"id":"https://openalex.org/W4366688467","doi":"https://doi.org/10.1177/14738716231167181","title":"Voronoi treemap in Manhattan distance and Chebyshev distance","display_name":"Voronoi treemap in Manhattan distance and Chebyshev distance","publication_year":2023,"publication_date":"2023-04-20","ids":{"openalex":"https://openalex.org/W4366688467","doi":"https://doi.org/10.1177/14738716231167181"},"language":"en","primary_location":{"id":"doi:10.1177/14738716231167181","is_oa":false,"landing_page_url":"https://doi.org/10.1177/14738716231167181","pdf_url":null,"source":{"id":"https://openalex.org/S55152591","display_name":"Information Visualization","issn_l":"1473-8716","issn":["1473-8716","1473-8724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Visualization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5062280616","display_name":"Yanchao Wang","orcid":"https://orcid.org/0000-0002-5482-8626"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Yan Chao Wang","raw_affiliation_strings":["Nanyang Technological University, Singapore, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-5482-8626","affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087584815","display_name":"Yidan Xing","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yidan Xing","raw_affiliation_strings":["Nanyang Technological University, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115590908","display_name":"Jie Zhang","orcid":"https://orcid.org/0009-0004-5173-9996"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jie Zhang","raw_affiliation_strings":["Nanyang Technological University, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062280616"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":0.695,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65303867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"3","first_page":"246","last_page":"264"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.9951000213623047,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.9744001626968384},{"id":"https://openalex.org/keywords/weighted-voronoi-diagram","display_name":"Weighted Voronoi diagram","score":0.7946375012397766},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.7005406022071838},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.694159746170044},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.4820759892463684},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.47195664048194885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4641714096069336},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.45856061577796936},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44029346108436584},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4208359718322754},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.41425377130508423},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2919003963470459},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25761258602142334},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15720334649085999},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.14001888036727905},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07354411482810974}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.9744001626968384},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.7946375012397766},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.7005406022071838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.694159746170044},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.4820759892463684},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.47195664048194885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4641714096069336},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.45856061577796936},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44029346108436584},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4208359718322754},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.41425377130508423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2919003963470459},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25761258602142334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15720334649085999},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.14001888036727905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07354411482810974},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/14738716231167181","is_oa":false,"landing_page_url":"https://doi.org/10.1177/14738716231167181","pdf_url":null,"source":{"id":"https://openalex.org/S55152591","display_name":"Information Visualization","issn_l":"1473-8716","issn":["1473-8716","1473-8724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Visualization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1509704371","https://openalex.org/W1710511026","https://openalex.org/W1905858685","https://openalex.org/W1966406768","https://openalex.org/W1984609374","https://openalex.org/W2001099600","https://openalex.org/W2002278016","https://openalex.org/W2020995339","https://openalex.org/W2023283825","https://openalex.org/W2027746986","https://openalex.org/W2035610579","https://openalex.org/W2043262812","https://openalex.org/W2045012623","https://openalex.org/W2046252734","https://openalex.org/W2048422125","https://openalex.org/W2048475323","https://openalex.org/W2051752778","https://openalex.org/W2070164574","https://openalex.org/W2072607341","https://openalex.org/W2091757707","https://openalex.org/W2106588364","https://openalex.org/W2121815329","https://openalex.org/W2135415614","https://openalex.org/W2142454908","https://openalex.org/W2165284015","https://openalex.org/W2290376740","https://openalex.org/W2604911573","https://openalex.org/W2624261308","https://openalex.org/W2750652038","https://openalex.org/W2753405889","https://openalex.org/W2774354559","https://openalex.org/W2779092424","https://openalex.org/W2910397750","https://openalex.org/W3042938618","https://openalex.org/W3133658790","https://openalex.org/W3141164029","https://openalex.org/W4243175349","https://openalex.org/W4293228482"],"related_works":["https://openalex.org/W2383087774","https://openalex.org/W2015548030","https://openalex.org/W2739428663","https://openalex.org/W2389906634","https://openalex.org/W1992160534","https://openalex.org/W4239527536","https://openalex.org/W2000970671","https://openalex.org/W2011450427","https://openalex.org/W2747977909","https://openalex.org/W1562406979"],"abstract_inverted_index":{"The":[0,108,226,264],"ordinary":[1,118,285],"Voronoi":[2,78,119,177,181,214,270,286,300],"treemap":[3,182,202,215],"generated":[4,243],"based":[5,256],"on":[6,132,257],"the":[7,12,17,61,65,69,89,92,104,115,133,156,159,173,195,201,213,230,239,248,268,284,299],"Euclidean":[8],"distance":[9,82,85,141,206,218],"function":[10],"has":[11,45],"flexibility":[13],"to":[14,63,103,161,171,192,210,236,298],"slightly":[15],"adjust":[16,194],"layout":[18,38,183,274],"when":[19],"visualizing":[20],"time-varying":[21],"hierarchical":[22],"data":[23],"for":[24,60,148],"better":[25,277],"visual":[26,278],"quality,":[27],"preserving":[28,32],"neighborhood":[29],"relationships,":[30],"and":[31,67,83,101,142,179,245,254,260,280,292],"a":[33,144,163,166,176,180],"stable":[34],"layout.":[35],"However,":[36],"its":[37],"formed":[39],"by":[40,188],"segments":[41,90],"with":[42],"arbitrary":[43],"orientations":[44,98],"poor":[46],"shape":[47,124,281],"stability":[48,282],"between":[49,136],"successive":[50],"layouts":[51,94,110,240],"at":[52],"different":[53,149],"time":[54],"indexes,":[55],"which":[56],"is":[57,158,169],"not":[58,112],"conducive":[59],"users":[62],"understand":[64],"plot":[66],"track":[68],"same":[70],"node.":[71],"In":[72],"this":[73],"paper,":[74],"we":[75,129,198],"propose":[76],"novel":[77],"treemaps":[79,271],"in":[80,91,139,204,216],"Manhattan":[81,140,205],"Chebyshev":[84,217],"respectively,":[86],"such":[87],"that":[88,200,267],"new":[93,109],"only":[95,113],"have":[96],"four":[97],"(horizontal,":[99],"vertical,":[100],"\u00b145\u00b0":[102],"[Formula:":[105],"see":[106],"text]-axis).":[107],"can":[111,184,207,241],"heritage":[114],"abilities":[116],"of":[117,152,229],"treemap,":[120],"but":[121,276,294],"preserve":[122,272],"good":[123],"stability.":[125],"To":[126],"achieve":[127],"this,":[128],"first":[130,234],"focus":[131],"weighted":[134],"bisector":[135,145,157],"two":[137,153],"sites":[138],"design":[143],"generation":[146],"method":[147,168,191],"weight":[150],"values":[151],"sites,":[154],"as":[155],"foundation":[160],"form":[162,172],"diagram.":[164,196],"Then":[165,247],"divide-and-conquer":[167],"utilized":[170],"bisectors":[174],"into":[175],"diagram,":[178],"be":[185,208,242],"finally":[186],"obtained":[187],"using":[189],"Lloyd\u2019s":[190],"iteratively":[193],"Moreover,":[197],"prove":[199],"algorithm":[203],"adjusted":[209],"also":[211,295],"generate":[212],"via":[219],"linear":[220],"transformation,":[221],"avoiding":[222],"designing":[223],"additional":[224],"algorithm.":[225],"computational":[227],"properties":[228,250],"proposed":[231,269],"methods":[232],"are":[233,251,290],"evaluated":[235,252],"check":[237],"whether":[238],"fast":[244],"accurately.":[246],"perceptual":[249],"quantitatively":[253],"qualitatively":[255],"quality":[258,279],"metrics":[259],"user":[261],"studies,":[262],"respectively.":[263],"results":[265],"demonstrate":[266],"similar":[273],"stability,":[275],"than":[283],"treemap.":[287],"Our":[288],"algorithms":[289],"simple":[291],"resolution-independent,":[293],"provide":[296],"alternatives":[297],"treemaps.":[301]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
