{"id":"https://openalex.org/W1960384938","doi":"https://doi.org/10.1109/cvpr.2015.7299106","title":"A stable multi-scale kernel for topological machine learning","display_name":"A stable multi-scale kernel for topological machine learning","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1960384938","doi":"https://doi.org/10.1109/cvpr.2015.7299106","mag":"1960384938"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2015.7299106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2015.7299106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","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/A5040080342","display_name":"Jan Reininghaus","orcid":null},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Jan Reininghaus","raw_affiliation_strings":["IST, Austria","IST, Austria;"],"affiliations":[{"raw_affiliation_string":"IST, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST, Austria;","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032047206","display_name":"Stefan Huber","orcid":"https://orcid.org/0000-0002-8871-5814"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stefan Huber","raw_affiliation_strings":["IST, Austria","IST, Austria;"],"affiliations":[{"raw_affiliation_string":"IST, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST, Austria;","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061971793","display_name":"Ulrich Bauer","orcid":"https://orcid.org/0000-0002-9683-0724"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Ulrich Bauer","raw_affiliation_strings":["TU, M\u00fcnchen","IST, Austria;"],"affiliations":[{"raw_affiliation_string":"TU, M\u00fcnchen","institution_ids":[]},{"raw_affiliation_string":"IST, Austria;","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086935121","display_name":"Roland Kwitt","orcid":"https://orcid.org/0000-0001-9947-4465"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Roland Kwitt","raw_affiliation_strings":["University of Salzburg, Austria","University of Salzburg Austria"],"affiliations":[{"raw_affiliation_string":"University of Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]},{"raw_affiliation_string":"University of Salzburg Austria","institution_ids":["https://openalex.org/I182212641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040080342"],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":null,"apc_paid":null,"fwci":26.8839,"has_fulltext":false,"cited_by_count":308,"citation_normalized_percentile":{"value":0.99752219,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"4741","last_page":"4748"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9362999796867371,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9053999781608582,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tree-kernel","display_name":"Tree kernel","score":0.841486930847168},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.8044275045394897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6168015003204346},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6042112112045288},{"id":"https://openalex.org/keywords/string-kernel","display_name":"String kernel","score":0.5785309672355652},{"id":"https://openalex.org/keywords/multiple-kernel-learning","display_name":"Multiple kernel learning","score":0.5689376592636108},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5633050203323364},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5562107563018799},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.5460666418075562},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.538877546787262},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5366923213005066},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.533357560634613},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4825243651866913},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4770504832267761},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47443854808807373},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.4637027382850647},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.44468817114830017},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4182330071926117},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3410572409629822},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26754701137542725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09289956092834473},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07922163605690002},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.0644221305847168}],"concepts":[{"id":"https://openalex.org/C140417398","wikidata":"https://www.wikidata.org/wiki/Q16933942","display_name":"Tree kernel","level":5,"score":0.841486930847168},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.8044275045394897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6168015003204346},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6042112112045288},{"id":"https://openalex.org/C55851704","wikidata":"https://www.wikidata.org/wiki/Q7623983","display_name":"String kernel","level":5,"score":0.5785309672355652},{"id":"https://openalex.org/C2776879701","wikidata":"https://www.wikidata.org/wiki/Q25048660","display_name":"Multiple kernel learning","level":4,"score":0.5689376592636108},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5633050203323364},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5562107563018799},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.5460666418075562},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.538877546787262},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5366923213005066},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.533357560634613},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4825243651866913},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4770504832267761},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47443854808807373},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.4637027382850647},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.44468817114830017},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4182330071926117},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3410572409629822},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26754701137542725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09289956092834473},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07922163605690002},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0644221305847168},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cvpr.2015.7299106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2015.7299106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W124643305","https://openalex.org/W191365292","https://openalex.org/W1481632020","https://openalex.org/W1487729220","https://openalex.org/W1541040343","https://openalex.org/W1560724230","https://openalex.org/W1569358572","https://openalex.org/W1575130722","https://openalex.org/W1579743691","https://openalex.org/W1991566301","https://openalex.org/W2010203208","https://openalex.org/W2030347560","https://openalex.org/W2036865416","https://openalex.org/W2037613900","https://openalex.org/W2099789128","https://openalex.org/W2100657858","https://openalex.org/W2109743529","https://openalex.org/W2113792310","https://openalex.org/W2122101130","https://openalex.org/W2124496089","https://openalex.org/W2126762337","https://openalex.org/W2133324003","https://openalex.org/W2136883589","https://openalex.org/W2147141800","https://openalex.org/W2149185044","https://openalex.org/W2151103935","https://openalex.org/W2153635508","https://openalex.org/W2159988601","https://openalex.org/W2160431995","https://openalex.org/W2163605009","https://openalex.org/W2962706934","https://openalex.org/W3140579943","https://openalex.org/W3195149063","https://openalex.org/W4255383393","https://openalex.org/W4300686066","https://openalex.org/W6607849749","https://openalex.org/W6629152740","https://openalex.org/W6634054468","https://openalex.org/W6677043478","https://openalex.org/W6679294498","https://openalex.org/W6681645188","https://openalex.org/W6681677808","https://openalex.org/W6684191040","https://openalex.org/W6837747933"],"related_works":["https://openalex.org/W4291669689","https://openalex.org/W2141199622","https://openalex.org/W2963372274","https://openalex.org/W2898882859","https://openalex.org/W4300176214","https://openalex.org/W2071590642","https://openalex.org/W2806943235","https://openalex.org/W1969447452","https://openalex.org/W2294612767","https://openalex.org/W1976730005"],"abstract_inverted_index":{"Topological":[0],"data":[1],"analysis":[2],"offers":[3],"a":[4,19,41,45,51],"rich":[5],"source":[6],"of":[7,55,94],"valuable":[8],"information":[9],"to":[10,23,74,99],"study":[11],"vision":[12],"problems.":[13],"Yet,":[14],"so":[15],"far":[16],"we":[17,38],"lack":[18],"theoretically":[20],"sound":[21],"connection":[22,42],"popular":[24],"kernel-based":[25],"learning":[26],"techniques,":[27],"such":[28,40],"as":[29],"kernel":[30,33,47,64],"SVMs":[31],"or":[32],"PCA.":[34],"In":[35],"this":[36,63],"work,":[37],"establish":[39],"by":[43],"designing":[44],"multi-scale":[46],"for":[48,83],"persistence":[49,110],"diagrams,":[50],"stable":[52],"summary":[53],"representation":[54],"topological":[56],"features":[57],"in":[58],"data.":[59],"We":[60],"show":[61,90],"that":[62,103],"is":[65,104],"positive":[66],"definite":[67],"and":[68,87],"prove":[69],"its":[70],"stability":[71],"with":[72],"respect":[73],"the":[75,95,107],"1-Wasserstein":[76],"distance.":[77],"Experiments":[78],"on":[79,106],"two":[80],"benchmark":[81],"datasets":[82],"3D":[84],"shape":[85],"classification/retrieval":[86],"texture":[88],"recognition":[89],"considerable":[91],"performance":[92],"gains":[93],"proposed":[96],"method":[97],"compared":[98],"an":[100],"alternative":[101],"approach":[102],"based":[105],"recently":[108],"introduced":[109],"landscapes.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":54},{"year":2020,"cited_by_count":35},{"year":2019,"cited_by_count":41},{"year":2018,"cited_by_count":29},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
