{"id":"https://openalex.org/W2549557354","doi":"https://doi.org/10.1109/ijcnn.2016.7727283","title":"Partially affine invariant back propagation","display_name":"Partially affine invariant back propagation","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2549557354","doi":"https://doi.org/10.1109/ijcnn.2016.7727283","mag":"2549557354"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2016.7727283","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2016.7727283","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-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/A5055364794","display_name":"Son Nguyen","orcid":"https://orcid.org/0000-0001-9409-4738"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Son Nguyen","raw_affiliation_strings":["Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082870488","display_name":"Kanishka Tyagi","orcid":"https://orcid.org/0000-0002-6104-1645"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kanishka Tyagi","raw_affiliation_strings":["Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062819305","display_name":"Parastoo Kheirkhah","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Parastoo Kheirkhah","raw_affiliation_strings":["Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114046112","display_name":"M.T. Manry","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Manry","raw_affiliation_strings":["Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The University of Texas at Arlington, Arlington, USA","institution_ids":["https://openalex.org/I189196454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055364794"],"corresponding_institution_ids":["https://openalex.org/I189196454"],"apc_list":null,"apc_paid":null,"fwci":0.4285,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.795175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"30","issue":null,"first_page":"811","last_page":"818"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9980999827384949,"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":0.9980999827384949,"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/T12676","display_name":"Machine Learning and ELM","score":0.9914000034332275,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.830805242061615},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.7958278656005859},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6844702363014221},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6312633752822876},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5457063317298889},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5320188999176025},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5197876691818237},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4855358302593231},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.43732452392578125},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42668479681015015},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.422078400850296},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4105954170227051},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.40471696853637695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3687554895877838},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.29114991426467896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2763168215751648},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18156147003173828},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.14005082845687866},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11151701211929321}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.830805242061615},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.7958278656005859},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6844702363014221},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6312633752822876},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5457063317298889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5320188999176025},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5197876691818237},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4855358302593231},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.43732452392578125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42668479681015015},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.422078400850296},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4105954170227051},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.40471696853637695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3687554895877838},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.29114991426467896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2763168215751648},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18156147003173828},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.14005082845687866},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11151701211929321},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2016.7727283","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2016.7727283","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W291003596","https://openalex.org/W1500731913","https://openalex.org/W1989513335","https://openalex.org/W2020416411","https://openalex.org/W2050067194","https://openalex.org/W2050900816","https://openalex.org/W2061933243","https://openalex.org/W2080180553","https://openalex.org/W2097238256","https://openalex.org/W2098265388","https://openalex.org/W2103459159","https://openalex.org/W2138149909","https://openalex.org/W2154029067","https://openalex.org/W2155482699","https://openalex.org/W2156373089","https://openalex.org/W2159032632","https://openalex.org/W2167554811","https://openalex.org/W2198965463","https://openalex.org/W2296319761","https://openalex.org/W2474855966","https://openalex.org/W3120740533","https://openalex.org/W3173138228","https://openalex.org/W4206366638","https://openalex.org/W4302081184"],"related_works":["https://openalex.org/W2026245502","https://openalex.org/W4318192194","https://openalex.org/W2070932288","https://openalex.org/W4221162014","https://openalex.org/W2937637171","https://openalex.org/W1964096161","https://openalex.org/W2572889128","https://openalex.org/W3091576739","https://openalex.org/W2892976100","https://openalex.org/W2958624776"],"abstract_inverted_index":{"A":[0],"novel":[1],"one":[2],"stage":[3],"batch":[4],"training":[5],"algorithm":[6],"is":[7,13,37,53],"proposed":[8],"in":[9],"which":[10],"Newton's":[11],"method":[12,25,49],"used":[14],"to":[15],"find":[16],"gains":[17],"on":[18],"inputs":[19],"and":[20,52,59],"hidden":[21],"unit":[22],"activations.":[23],"The":[24],"has":[26],"far":[27],"less":[28],"computational":[29],"complexity":[30],"than":[31,40,56],"Leverberg-Marquart":[32],"because":[33],"the":[34,48],"method's":[35],"Hessian":[36],"much":[38],"smaller":[39],"that":[41,47],"of":[42],"LM.":[43],"Numerical":[44],"results":[45],"shows":[46],"converges":[50],"faster":[51],"more":[54],"stable":[55],"conjugate":[57],"gradient":[58],"BFGS.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}