{"id":"https://openalex.org/W4400421421","doi":"https://doi.org/10.3390/a17070296","title":"Hardness and Approximability of Dimension Reduction on the Probability Simplex","display_name":"Hardness and Approximability of Dimension Reduction on the Probability Simplex","publication_year":2024,"publication_date":"2024-07-06","ids":{"openalex":"https://openalex.org/W4400421421","doi":"https://doi.org/10.3390/a17070296"},"language":"en","primary_location":{"id":"doi:10.3390/a17070296","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070296","pdf_url":"https://www.mdpi.com/1999-4893/17/7/296/pdf?version=1720250529","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/17/7/296/pdf?version=1720250529","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094034761","display_name":"Roberto Bruno","orcid":"https://orcid.org/0000-0001-6039-2075"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Roberto Bruno","raw_affiliation_strings":["Department of Computer Science, University of Salerno, 84084 Fisciano, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Salerno, 84084 Fisciano, Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5094034761"],"corresponding_institution_ids":["https://openalex.org/I131729948"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.7088,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74609618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"17","issue":"7","first_page":"296","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9926000237464905,"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":0.9926000237464905,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9837999939918518,"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"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9830999970436096,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.7996171712875366},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.675512969493866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.651210367679596},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6001682281494141},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5022706985473633},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.49645310640335083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3406507670879364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19503816962242126},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10285139083862305},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09165027737617493}],"concepts":[{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.7996171712875366},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.675512969493866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.651210367679596},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6001682281494141},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5022706985473633},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.49645310640335083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3406507670879364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19503816962242126},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10285139083862305},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09165027737617493}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a17070296","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070296","pdf_url":"https://www.mdpi.com/1999-4893/17/7/296/pdf?version=1720250529","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2407.16352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.16352","pdf_url":"https://arxiv.org/pdf/2407.16352","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":"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"},{"id":"pmh:oai:doaj.org/article:401b086da30c4aba99dee32113d53d3b","is_oa":true,"landing_page_url":"https://doaj.org/article/401b086da30c4aba99dee32113d53d3b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 17, Iss 7, p 296 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a17070296","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17070296","pdf_url":"https://www.mdpi.com/1999-4893/17/7/296/pdf?version=1720250529","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400421421.pdf","grobid_xml":"https://content.openalex.org/works/W4400421421.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1543921836","https://openalex.org/W1828332764","https://openalex.org/W1965555277","https://openalex.org/W2009990213","https://openalex.org/W2044925719","https://openalex.org/W2052958516","https://openalex.org/W2054631532","https://openalex.org/W2079148437","https://openalex.org/W2080686589","https://openalex.org/W2085294315","https://openalex.org/W2096623985","https://openalex.org/W2109518176","https://openalex.org/W2112883966","https://openalex.org/W2114473842","https://openalex.org/W2117920736","https://openalex.org/W2141585001","https://openalex.org/W2512147363","https://openalex.org/W2579406944","https://openalex.org/W2782983924","https://openalex.org/W2953851932","https://openalex.org/W2963484654","https://openalex.org/W2963705438","https://openalex.org/W2966263989","https://openalex.org/W3035001865","https://openalex.org/W4221141587","https://openalex.org/W4280640767","https://openalex.org/W4313598801","https://openalex.org/W4321854339","https://openalex.org/W4391451551","https://openalex.org/W6638427228","https://openalex.org/W6674181579","https://openalex.org/W6681005949","https://openalex.org/W6766218515","https://openalex.org/W6850471101"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2063021680","https://openalex.org/W3176621072","https://openalex.org/W2357922472","https://openalex.org/W2384278689","https://openalex.org/W2563365141","https://openalex.org/W2386777115","https://openalex.org/W2888513445","https://openalex.org/W2376265369","https://openalex.org/W2383374609"],"abstract_inverted_index":{"Dimension":[0],"reduction":[1,49],"is":[2,30,71,90],"a":[3,10,14],"technique":[4],"used":[5],"to":[6,18,63,74],"transform":[7],"data":[8],"from":[9],"high-dimensional":[11],"space":[12],"into":[13],"lower-dimensional":[15],"space,":[16],"aiming":[17],"retain":[19],"as":[20,26,80],"much":[21],"of":[22,83],"the":[23,46,65,72,77,81,88],"original":[24],"information":[25],"possible.":[27],"This":[28],"approach":[29],"crucial":[31],"in":[32],"many":[33],"disciplines":[34],"like":[35],"engineering,":[36],"biology,":[37],"astronomy,":[38],"and":[39,57,93],"economics.":[40],"In":[41],"this":[42],"paper,":[43],"we":[44,61,94],"consider":[45],"following":[47],"dimensionality":[48],"instance:":[50],"Given":[51],"an":[52,58,96],"n-dimensional":[53],"probability":[54,67],"distribution":[55,68],"p":[56],"integer":[59],"m<n,":[60],"aim":[62],"find":[64],"m-dimensional":[66],"q":[69],"that":[70,87],"closest":[73],"p,":[75],"using":[76],"Kullback\u2013Leibler":[78],"divergence":[79],"measure":[82],"closeness.":[84],"We":[85],"prove":[86],"problem":[89],"strongly":[91],"NP-hard,":[92],"present":[95],"approximation":[97],"algorithm":[98],"for":[99],"it.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}