{"id":"https://openalex.org/W2804126069","doi":null,"title":"H-CNNs: Convolutional Neural Networks for Riemannian Homogeneous Spaces.","display_name":"H-CNNs: Convolutional Neural Networks for Riemannian Homogeneous Spaces.","publication_year":2018,"publication_date":"2018-05-14","ids":{"openalex":"https://openalex.org/W2804126069","mag":"2804126069"},"language":"en","primary_location":{"id":"mag:2804126069","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1805.05487","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1805.05487","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025100345","display_name":"Rudrasis Chakraborty","orcid":"https://orcid.org/0000-0002-0448-911X","observed_orcids":["https://orcid.org/0000-0002-0448-911X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rudrasis Chakraborty","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101120703","display_name":"Monami Banerjee","orcid":"https://orcid.org/0009-0004-8441-758X","observed_orcids":["https://orcid.org/0009-0004-8441-758X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Monami Banerjee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016378470","display_name":"Baba C. Vemuri","orcid":"https://orcid.org/0000-0002-1400-5844","observed_orcids":["https://orcid.org/0000-0002-1400-5844"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baba C. Vemuri","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1400-5844","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.37380000948905945,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.37380000948905945,"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/T10320","display_name":"Neural Networks and Applications","score":0.23739999532699585,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.03920000046491623,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/spherical-convolutional-neural-networks","display_name":"spherical convolutional neural networks","score":0.7480000257492065},{"id":"https://openalex.org/keywords/rotational-equivariance","display_name":"rotational equivariance","score":0.8550000190734863},{"id":"https://openalex.org/keywords/symmetric-positive-definite-matrices","display_name":"symmetric positive definite matrices","score":0.6779999732971191},{"id":"https://openalex.org/keywords/product-manifolds","display_name":"product manifolds","score":0.6779999732971191},{"id":"https://openalex.org/keywords/diffusion-mri","display_name":"diffusion MRI","score":0.5379999876022339},{"id":"https://openalex.org/keywords/manifold-learning","display_name":"manifold learning","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6270368099212646},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.6149570941925049},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5809119343757629},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5785797834396362},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5723572969436646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5010321140289307},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.47420504689216614},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.46746826171875},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4608764946460724},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3600512146949768},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31786468625068665},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30926263332366943},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23341426253318787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2171899378299713},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19253754615783691},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.062398940324783325},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2804126069","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1805.05487","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2804126069","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1805.05487","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W603908379","https://openalex.org/W1589163079","https://openalex.org/W1661897762","https://openalex.org/W2003513369","https://openalex.org/W2017262657","https://openalex.org/W2107790757","https://openalex.org/W2112796928","https://openalex.org/W2576915720","https://openalex.org/W2751473119","https://openalex.org/W2754770188","https://openalex.org/W2785397276","https://openalex.org/W3118608800","https://openalex.org/W4394667618"],"related_works":["https://openalex.org/W2886244690","https://openalex.org/W3097357697","https://openalex.org/W7214767671","https://openalex.org/W2900364424","https://openalex.org/W3127922021","https://openalex.org/W3091786697","https://openalex.org/W7166158565","https://openalex.org/W7133240933","https://openalex.org/W4299822022","https://openalex.org/W2965554687"],"abstract_inverted_index":{"Convolutional":[0],"neural":[1],"networks":[2],"are":[3,152,156],"ubiquitous":[4],"in":[5,159],"Machine":[6],"Learning":[7],"applications":[8],"for":[9],"solving":[10],"a":[11,59,164],"variety":[12],"of":[13,43,53,86,125,135,147],"problems.":[14],"They":[15],"however":[16],"can":[17],"not":[18],"be":[19],"used":[20],"as":[21,32,79],"is":[22,93],"when":[23],"data":[24,56,130],"naturally":[25],"reside":[26],"on":[27,58,132],"commonly":[28,116,157],"encountered":[29,117,158],"manifolds":[30,118,155],"such":[31],"the":[33,35,39,41,90,97,107,120,133,144],"sphere,":[34],"special":[36],"orthogonal":[37],"group,":[38],"Grassmanian,":[40],"manifold":[42,134,146],"symmetric":[44,139],"positive":[45,140],"definite":[46,141],"matrices":[47,142],"and":[48,143],"others.":[49],"Most":[50],"recently,":[51],"generalization":[52],"CNNs":[54,81,92],"to":[55,77,109],"residing":[57],"sphere":[60],"has":[61],"been":[62],"reported":[63],"by":[64,70],"some":[65],"research":[66],"groups,":[67],"which":[68],"go":[69],"several":[71],"names":[72],"but":[73],"we":[74,104],"will":[75],"refer":[76],"them":[78],"spherical":[80],"(SCNNs).":[82],"The":[83],"key":[84],"property":[85],"SCNNs":[87,108],"distinct":[88],"from":[89],"standard":[91],"that":[94,113],"they":[95],"exhibit":[96],"rotational":[98],"equivariance":[99],"property.":[100],"In":[101],"this":[102],"paper,":[103],"theoretically":[105],"generalize":[106],"Riemannian":[110],"homogeneous":[111],"manifolds,":[112],"include":[114],"many":[115],"including":[119],"aforementioned":[121],"example":[122],"manifolds.":[123],"Proof":[124],"concept":[126],"experiments":[127],"involving":[128],"synthetic":[129],"generated":[131],"$(3":[136],"\\times":[137,149],"3)$":[138],"product":[145],"$\\mathbf{R}^+":[148],"\\mathbf{S}^2$":[150],"respectively,":[151],"presented.":[153],"These":[154],"diffusion":[160],"magnetic":[161],"resonance":[162],"imaging,":[163],"non-invasive":[165],"medical":[166],"imaging":[167],"modality.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2018-06-01T00:00:00"}