{"id":"https://openalex.org/W7134072909","doi":"https://doi.org/10.3390/info17030265","title":"A Comparative Study of Embedding Methods for Clustering Mathematical Functions","display_name":"A Comparative Study of Embedding Methods for Clustering Mathematical Functions","publication_year":2026,"publication_date":"2026-03-06","ids":{"openalex":"https://openalex.org/W7134072909","doi":"https://doi.org/10.3390/info17030265"},"language":"en","primary_location":{"id":"doi:10.3390/info17030265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info17030265","pdf_url":"https://www.mdpi.com/2078-2489/17/3/265/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2078-2489/17/3/265/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049700581","display_name":"H. Al-Jabbouli","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hasan Aljabbouli","raw_affiliation_strings":["Department of Computer Science, Courant Institute School, New York University, New York, NY 10012, USA"],"raw_orcid":"https://orcid.org/0009-0002-5775-2484","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Courant Institute School, New York University, New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035129320","display_name":"Ahmad B. Alkhodre","orcid":"https://orcid.org/0000-0001-6168-3552"},"institutions":[{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad B. Alkhodre","raw_affiliation_strings":["Department of Information Technology, Faculty of Computer and Information Systems, Islamic University of Madinah, Madinah 42351, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6168-3552","affiliations":[{"raw_affiliation_string":"Department of Information Technology, Faculty of Computer and Information Systems, Islamic University of Madinah, Madinah 42351, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35174801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"3","first_page":"265","last_page":"265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.13359999656677246,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.13359999656677246,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.08839999884366989,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.06610000133514404,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6898000240325928},{"id":"https://openalex.org/keywords/discriminative-model","display_name":"Discriminative model","score":0.6862000226974487},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6549999713897705},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5325999855995178},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5109999775886536},{"id":"https://openalex.org/keywords/silhouette","display_name":"Silhouette","score":0.47769999504089355},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4740999937057495},{"id":"https://openalex.org/keywords/feature-learning","display_name":"Feature learning","score":0.46309998631477356},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.44859999418258667}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.7106999754905701},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6898000240325928},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.6862000226974487},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6549999713897705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.545199990272522},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5325999855995178},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5109999775886536},{"id":"https://openalex.org/C58103923","wikidata":"https://www.wikidata.org/wiki/Q2286025","display_name":"Silhouette","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4699999988079071},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.4205999970436096},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.35370001196861267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3368000090122223},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C58973888","wikidata":"https://www.wikidata.org/wiki/Q1041418","display_name":"Semi-supervised learning","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/info17030265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info17030265","pdf_url":"https://www.mdpi.com/2078-2489/17/3/265/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8dda2162ceeb4a839d55463183042614","is_oa":true,"landing_page_url":"https://doaj.org/article/8dda2162ceeb4a839d55463183042614","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":"Information, Vol 17, Iss 3, p 265 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/info17030265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info17030265","pdf_url":"https://www.mdpi.com/2078-2489/17/3/265/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"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":"Information","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7873676419258118,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7134072909.pdf","grobid_xml":"https://content.openalex.org/works/W7134072909.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W82869218","https://openalex.org/W1987971958","https://openalex.org/W2270663840","https://openalex.org/W4239025696","https://openalex.org/W4292156489","https://openalex.org/W4310225030","https://openalex.org/W4310494058","https://openalex.org/W4385218718","https://openalex.org/W4386836227","https://openalex.org/W4391784408","https://openalex.org/W4402922361","https://openalex.org/W4403984767"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3],"comprehensive":[4],"comparative":[5],"study":[6],"of":[7,89],"deep":[8],"learning":[9,64,92],"approaches":[10],"for":[11,94],"clustering":[12],"mathematical":[13,51,95],"functions":[14,43],"based":[15],"on":[16],"their":[17],"behavioral":[18],"patterns.":[19],"We":[20],"investigate":[21],"three":[22],"distinct":[23],"embedding":[24],"strategies:":[25],"autoencoder-based":[26],"unsupervised":[27],"learning,":[28],"supervised":[29,63],"classification":[30],"with":[31,65],"learned":[32],"embeddings,":[33,74],"and":[34,56],"direct":[35],"convolutional":[36],"feature":[37],"extraction.":[38],"Each":[39],"approach":[40],"transforms":[41],"continuous":[42],"into":[44,85],"meaningful":[45],"vector":[46],"representations":[47],"that":[48,62],"capture":[49],"essential":[50],"characteristics.":[52],"Through":[53],"extensive":[54],"experimentation":[55],"multiple":[57],"visualization":[58],"techniques,":[59],"we":[60],"demonstrate":[61],"explicit":[66],"function":[67,96],"type":[68],"guidance":[69],"produces":[70],"the":[71,86],"most":[72],"discriminative":[73],"achieving":[75],"average":[76],"silhouette":[77],"score":[78],"0.6.":[79],"Our":[80],"findings":[81],"provide":[82],"valuable":[83],"insights":[84],"relative":[87],"effectiveness":[88],"different":[90],"representation":[91],"paradigms":[93],"analysis.":[97]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-07T00:00:00"}