{"id":"https://openalex.org/W2968290877","doi":"https://doi.org/10.1007/978-3-030-26980-7_36","title":"Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences","display_name":"Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2968290877","doi":"https://doi.org/10.1007/978-3-030-26980-7_36","mag":"2968290877"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-26980-7_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-26980-7_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5014179168","display_name":"Erika Gomes-Gon\u00e7alves","orcid":"https://orcid.org/0000-0002-3633-776X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erika Gomes-Gon\u00e7alves","raw_affiliation_strings":["Independent Consultant, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-3633-776X","affiliations":[{"raw_affiliation_string":"Independent Consultant, Madrid, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026656556","display_name":"Henryk Gzyl","orcid":"https://orcid.org/0000-0002-3781-8848"},"institutions":[{"id":"https://openalex.org/I4210153497","display_name":"Institute of Advanced Studies in Administration","ror":"https://ror.org/0580grj78","country_code":"VE","type":"education","lineage":["https://openalex.org/I4210153497"]}],"countries":["VE"],"is_corresponding":false,"raw_author_name":"Henryk Gzyl","raw_affiliation_strings":["Centro de Finanzas IESA, Caracas, Venezuela"],"raw_orcid":"https://orcid.org/0000-0002-3781-8848","affiliations":[{"raw_affiliation_string":"Centro de Finanzas IESA, Caracas, Venezuela","institution_ids":["https://openalex.org/I4210153497"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061293973","display_name":"Frank Nielsen","orcid":"https://orcid.org/0000-0001-5728-0726"},"institutions":[{"id":"https://openalex.org/I4210122684","display_name":"Sony Computer Science Laboratories","ror":"https://ror.org/02nc46417","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210122684"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Frank Nielsen","raw_affiliation_strings":["Sony Computer Science Laboratories, Inc., Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0001-5728-0726","affiliations":[{"raw_affiliation_string":"Sony Computer Science Laboratories, Inc., Tokyo, Japan","institution_ids":["https://openalex.org/I4210122684"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061293973"],"corresponding_institution_ids":["https://openalex.org/I4210122684"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.5953,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.83178266,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"351","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.968999981880188,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.668509840965271},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6407936811447144},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5466071963310242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5396623015403748},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5329182147979736},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5070464611053467},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4760865271091461},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.47326067090034485},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.42352113127708435},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.42330437898635864},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.42146602272987366},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.41846388578414917},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33868134021759033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3326473832130432},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29178154468536377},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1874871850013733},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17016014456748962},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13462060689926147},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.09274446964263916}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.668509840965271},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6407936811447144},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5466071963310242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5396623015403748},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5329182147979736},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5070464611053467},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4760865271091461},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.47326067090034485},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.42352113127708435},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.42330437898635864},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.42146602272987366},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.41846388578414917},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33868134021759033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3326473832130432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29178154468536377},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1874871850013733},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17016014456748962},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13462060689926147},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.09274446964263916},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-26980-7_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-26980-7_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W36455802","https://openalex.org/W595145996","https://openalex.org/W1567180517","https://openalex.org/W1573082642","https://openalex.org/W2040711469","https://openalex.org/W2046947077","https://openalex.org/W2075057405","https://openalex.org/W2116327295","https://openalex.org/W2121133842","https://openalex.org/W2887991093","https://openalex.org/W2888146396","https://openalex.org/W4300998111","https://openalex.org/W6689075165","https://openalex.org/W6689676704"],"related_works":["https://openalex.org/W4295816620","https://openalex.org/W2106579555","https://openalex.org/W2791826772","https://openalex.org/W2074269613","https://openalex.org/W3159542909","https://openalex.org/W4291625303","https://openalex.org/W2901017798","https://openalex.org/W4320853694","https://openalex.org/W2737579912","https://openalex.org/W1976330683"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
