{"id":"https://openalex.org/W2396840719","doi":"https://doi.org/10.1109/icassp.2016.7472916","title":"Persistent homology of toroidal sliding window embeddings","display_name":"Persistent homology of toroidal sliding window embeddings","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2396840719","doi":"https://doi.org/10.1109/icassp.2016.7472916","mag":"2396840719"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2016.7472916","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2016.7472916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","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/A5017700107","display_name":"Jos\u00e9 A. Perea","orcid":"https://orcid.org/0000-0002-6440-5096"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jose A. Perea","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017700107"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":6.4651,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.96686864,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"6435","last_page":"6439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9674999713897705,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.916700005531311,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/embedding","display_name":"Embedding","score":0.7724658250808716},{"id":"https://openalex.org/keywords/harmonics","display_name":"Harmonics","score":0.6880382895469666},{"id":"https://openalex.org/keywords/toroid","display_name":"Toroid","score":0.661662220954895},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.618964433670044},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.5547908544540405},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5070056915283203},{"id":"https://openalex.org/keywords/window-function","display_name":"Window function","score":0.48097503185272217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47748371958732605},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.47530779242515564},{"id":"https://openalex.org/keywords/sliding-window-protocol","display_name":"Sliding window protocol","score":0.4547925591468811},{"id":"https://openalex.org/keywords/window","display_name":"Window (computing)","score":0.45384636521339417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4141392409801483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.376424103975296},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32962390780448914},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27257484197616577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2721855044364929},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2685755491256714},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15903976559638977},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0982813835144043},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09297588467597961},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06213253736495972}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7724658250808716},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.6880382895469666},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.661662220954895},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.618964433670044},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5547908544540405},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5070056915283203},{"id":"https://openalex.org/C140101238","wikidata":"https://www.wikidata.org/wiki/Q1404885","display_name":"Window function","level":3,"score":0.48097503185272217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47748371958732605},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.47530779242515564},{"id":"https://openalex.org/C102392041","wikidata":"https://www.wikidata.org/wiki/Q592860","display_name":"Sliding window protocol","level":3,"score":0.4547925591468811},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.45384636521339417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4141392409801483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.376424103975296},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32962390780448914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27257484197616577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2721855044364929},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2685755491256714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15903976559638977},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0982813835144043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09297588467597961},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06213253736495972},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2016.7472916","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2016.7472916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W178103694","https://openalex.org/W1486497799","https://openalex.org/W1549386224","https://openalex.org/W1575834508","https://openalex.org/W1803377658","https://openalex.org/W1872613111","https://openalex.org/W1900583485","https://openalex.org/W1990251386","https://openalex.org/W2013146176","https://openalex.org/W2064195766","https://openalex.org/W2071391326","https://openalex.org/W2075019393","https://openalex.org/W2102368730","https://openalex.org/W2123774638","https://openalex.org/W3040586665","https://openalex.org/W4297756508","https://openalex.org/W6607365138","https://openalex.org/W6639902759"],"related_works":["https://openalex.org/W3128725485","https://openalex.org/W2797851727","https://openalex.org/W3159198591","https://openalex.org/W4293460689","https://openalex.org/W2013173893","https://openalex.org/W2163803384","https://openalex.org/W2321297009","https://openalex.org/W4313654668","https://openalex.org/W3099927136","https://openalex.org/W44066255"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper":[2],"we":[3],"study":[4],"the":[5,51,61],"persistent":[6,63],"homology":[7],"of":[8,12,21,53],"sliding":[9,35],"window":[10,36,54],"embeddings":[11],"quasi-periodic":[13],"signals.":[14],"That":[15],"is,":[16],"functions":[17],"which":[18,49],"are":[19,41],"sums":[20],"harmonics":[22],"with":[23],"different":[24],"periods,":[25],"and":[26,56,59],"in":[27,38],"particular,":[28],"those":[29],"having":[30],"incommensurate":[31],"frequencies.":[32],"The":[33],"resulting":[34],"point-clouds,":[37],"case,":[40],"(dense":[42],"in)":[43],"high-dimensional":[44],"tori.":[45],"We":[46],"prove":[47],"theorems":[48],"guide":[50],"choice":[52],"size":[55],"embedding":[57],"dimension,":[58],"describe":[60],"associated":[62],"homology.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-04T09:10:02.777135","created_date":"2025-10-10T00:00:00"}
