{"id":"https://openalex.org/W2113787552","doi":null,"title":"Separating features from noise with persistence and statistics","display_name":"Separating features from noise with persistence and statistics","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2113787552","mag":"2113787552"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.5602","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.5602","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/%7Ebeiwang/publications/ThesisBW.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5100349957","display_name":"Bei Wang","orcid":"https://orcid.org/0000-0002-9530-0385","observed_orcids":["https://orcid.org/0000-0002-9530-0385"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bei Wang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9530-0385","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5100349957"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"persistent homology","score":0.8489999771118164},{"id":"https://openalex.org/keywords/scan-statistics","display_name":"scan statistics","score":0.7160000205039978},{"id":"https://openalex.org/keywords/graph-clustering","display_name":"graph clustering","score":0.7739999890327454},{"id":"https://openalex.org/keywords/piecewise-linear-functions","display_name":"piecewise linear functions","score":0.7329999804496765},{"id":"https://openalex.org/keywords/triangulation","display_name":"triangulation","score":0.9409999847412109},{"id":"https://openalex.org/keywords/local-maxima","display_name":"local maxima","score":0.8539999723434448},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.8830000162124634},{"id":"https://openalex.org/keywords/feature-detection","display_name":"feature detection","score":0.503000020980835},{"id":"https://openalex.org/keywords/point-clouds","display_name":"point clouds","score":0.8109999895095825}],"concepts":[{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.6723673939704895},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6454715728759766},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.538378894329071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3813055157661438},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.34674888849258423},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3456844389438629},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3109411597251892},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23073449730873108},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16970616579055786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16377171874046326},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.5602","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.5602","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/%7Ebeiwang/publications/ThesisBW.pdf","raw_type":"text"},{"id":"pmh:oai:dukespace.lib.duke.edu:10161/2982","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10161/2982","pdf_url":null,"source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dissertation"},{"id":"mag:2113787552","doi":null,"is_oa":false,"landing_page_url":"https://dukespace.lib.duke.edu/dspace/bitstream/10161/2982/1/D_Wang_Bei_a_2010.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":106,"referenced_works":["https://openalex.org/W120774042","https://openalex.org/W186822082","https://openalex.org/W189016807","https://openalex.org/W204424931","https://openalex.org/W632115384","https://openalex.org/W1486210143","https://openalex.org/W1486817521","https://openalex.org/W1496383623","https://openalex.org/W1500527815","https://openalex.org/W1515675992","https://openalex.org/W1516289958","https://openalex.org/W1542057543","https://openalex.org/W1570205513","https://openalex.org/W1573091022","https://openalex.org/W1586785555","https://openalex.org/W1591378753","https://openalex.org/W1599969036","https://openalex.org/W1614760033","https://openalex.org/W1626653188","https://openalex.org/W1646289414","https://openalex.org/W1660264423","https://openalex.org/W1680861744","https://openalex.org/W1795607446","https://openalex.org/W1929593512","https://openalex.org/W1967070686","https://openalex.org/W1970379663","https://openalex.org/W1971421925","https://openalex.org/W1974973278","https://openalex.org/W1978690156","https://openalex.org/W1985625141","https://openalex.org/W1991370590","https://openalex.org/W1993946385","https://openalex.org/W1994149163","https://openalex.org/W1996931690","https://openalex.org/W2002151188","https://openalex.org/W2008318377","https://openalex.org/W2008620264","https://openalex.org/W2009940349","https://openalex.org/W2012205791","https://openalex.org/W2015953751","https://openalex.org/W2017128277","https://openalex.org/W2018777660","https://openalex.org/W2025543856","https://openalex.org/W2028270345","https://openalex.org/W2030075935","https://openalex.org/W2037613900","https://openalex.org/W2046305987","https://openalex.org/W2047474521","https://openalex.org/W2047940964","https://openalex.org/W2051358370","https://openalex.org/W2054902478","https://openalex.org/W2056761334","https://openalex.org/W2059217294","https://openalex.org/W2061083393","https://openalex.org/W2063776392","https://openalex.org/W2063831812","https://openalex.org/W2071569218","https://openalex.org/W2083772019","https://openalex.org/W2089458547","https://openalex.org/W2090807899","https://openalex.org/W2091452023","https://openalex.org/W2093012474","https://openalex.org/W2095072199","https://openalex.org/W2095966322","https://openalex.org/W2096631127","https://openalex.org/W2096765209","https://openalex.org/W2097308346","https://openalex.org/W2098646941","https://openalex.org/W2104809968","https://openalex.org/W2107605271","https://openalex.org/W2112976607","https://openalex.org/W2114030927","https://openalex.org/W2115896258","https://openalex.org/W2120176508","https://openalex.org/W2120672285","https://openalex.org/W2121564430","https://openalex.org/W2121947440","https://openalex.org/W2122101130","https://openalex.org/W2123538828","https://openalex.org/W2125179362","https://openalex.org/W2128366083","https://openalex.org/W2132629607","https://openalex.org/W2135957668","https://openalex.org/W2136850043","https://openalex.org/W2140273660","https://openalex.org/W2140788524","https://openalex.org/W2145076372","https://openalex.org/W2149304112","https://openalex.org/W2149906774","https://openalex.org/W2151936673","https://openalex.org/W2157878484","https://openalex.org/W2159998603","https://openalex.org/W2161184224","https://openalex.org/W2164928285","https://openalex.org/W2177347332","https://openalex.org/W2434205482","https://openalex.org/W2769133055","https://openalex.org/W2799002609","https://openalex.org/W2799087070","https://openalex.org/W2912268514","https://openalex.org/W3013843370","https://openalex.org/W3040586665","https://openalex.org/W3139495523","https://openalex.org/W3140579943","https://openalex.org/W4235295213","https://openalex.org/W4251465045"],"related_works":["https://openalex.org/W2797851727","https://openalex.org/W2294381658","https://openalex.org/W7100667957","https://openalex.org/W6959599005","https://openalex.org/W1957046493","https://openalex.org/W39770168","https://openalex.org/W7097774470","https://openalex.org/W3004701186","https://openalex.org/W7095440026","https://openalex.org/W2031793741"],"abstract_inverted_index":{"In":[0],"this":[1,71],"thesis,":[2],"we":[3,186],"explore":[4],"techniques":[5],"in":[6,36,58,108,119,144,168,221],"statistics":[7,88],"and":[8,21,30,80,228,284,288],"persistent":[9,230],"homology,":[10],"which":[11,201],"detect":[12],"features":[13,146],"among":[14,106],"data":[15],"sets":[16],"such":[17,78,175,237],"as":[18],"graphs,":[19],"triangulations":[20,97,149],"point":[22,194,220],"cloud.":[23],"We":[24,38,63,73,85,101,111,121,153,173,213,232,276,292],"accompany":[25],"our":[26],"theorems":[27],"with":[28,40,162,177,257,274],"algorithms":[29,75],"experiments,":[31],"to":[32,50,157,204,223,269],"demonstrate":[33],"their":[34],"effectiveness":[35,235],"practice.":[37],"start":[39],"the":[41,52,96,109,125,130,148,178,183,205,215,234,244,254,258,271,282],"derivation":[42],"of":[43,55,60,98,132,147,150,182,218,236,246],"graph":[44],"scan":[45],"statistics,":[46],"a":[47,56,133,163,188,193,198,209,219],"measure":[48],"useful":[49,143],"assess":[51,214,270],"statistical":[53],"significance":[54],"subgraph":[57],"terms":[59],"edge":[61],"density.":[62],"cluster":[64],"graphs":[65],"into":[66],"densely-connected":[67],"subgraphs":[68],"based":[69],"on":[70,82,89,95,129,295],"measure.":[72],"give":[74],"for":[76,91,116],"finding":[77],"clusterings":[79],"experiment":[81,294],"real-world":[83],"data.":[84,298],"next":[86],"study":[87,187],"persistence,":[90],"piecewise-linear":[92],"functions":[93],"defined":[94,128],"topological":[99,250],"spaces.":[100],"derive":[102],"persistence":[103,118,140,286],"pairing":[104,141],"probabilities":[105],"vertices":[107],"triangulation.":[110],"also":[112],"provide":[113],"upper":[114],"bounds":[115],"total":[117,179],"expectation.":[120],"continue":[122],"by":[123,139],"examining":[124],"elevation":[126],"function":[127],"triangulation":[131],"surface.":[134],"Its":[135],"local":[136,160,216,272],"maxima":[137],"obtained":[138],"are":[142],"describing":[145],"protein":[151],"surfaces.":[152,184],"describe":[154,277],"an":[155,278],"algorithm":[156,279],"compute":[158],"these":[159],"maxima,":[161],"run-time":[164],"ten-thousand":[165],"times":[166],"faster":[167],"practice":[169],"than":[170],"previous":[171],"method.":[172],"connect":[174],"improvement":[176],"Gaussian":[180],"curvature":[181],"Finally,":[185],"stratification":[189],"learning":[190],"problem:":[191],"given":[192,210],"cloud":[195],"sampled":[196],"from":[197],"stratified":[199],"space,":[200],"points":[202],"belong":[203],"same":[206],"strata,":[207],"at":[208],"scale":[211],"level?":[212],"structure":[217,273],"relation":[222],"its":[224,290],"neighbors":[225],"using":[226],"kernel":[227,283],"cokernel":[229,285],"homology.":[231],"prove":[233,289],"assessment":[238],"through":[239],"several":[240],"inference":[241,251,264],"theorems,":[242],"under":[243],"assumption":[245],"dense":[247],"sample.":[248],"The":[249,262],"theorem":[252,265],"relates":[253],"sample":[255,267],"density":[256],"homological":[259],"feature":[260],"size.":[261],"probabilistic":[263],"provides":[266],"estimates":[268],"confidence.":[275],"that":[280],"computes":[281],"diagrams":[287],"correctness.":[291],"further":[293],"simple":[296],"synthetic":[297]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}