{"id":"https://openalex.org/W7160036519","doi":"https://doi.org/10.48550/arxiv.2605.00069","title":"Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Series","display_name":"Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Series","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7160036519","doi":"https://doi.org/10.48550/arxiv.2605.00069"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.00069","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.00069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103057163","display_name":"Christopher Holder","orcid":"https://orcid.org/0000-0001-9571-3764"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Holder, Christopher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125432569","display_name":"Anthony Bagnall","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bagnall, Anthony","raw_affiliation_strings":[],"raw_orcid":null,"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":0,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T13702","display_name":"Machine Learning in Healthcare","score":0.0008999999845400453,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.0003000000142492354,"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/dynamic-time-warping","display_name":"Dynamic time warping","score":0.8970999717712402},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6011999845504761},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5979999899864197},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5709999799728394},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.553600013256073},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5446000099182129},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.47780001163482666},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.43220001459121704}],"concepts":[{"id":"https://openalex.org/C88516994","wikidata":"https://www.wikidata.org/wiki/Q1268863","display_name":"Dynamic time warping","level":2,"score":0.8970999717712402},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6011999845504761},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5979999899864197},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5709999799728394},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.553600013256073},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5446000099182129},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5299000144004822},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45980000495910645},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42809998989105225},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.4092999994754791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3790000081062317},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C157202957","wikidata":"https://www.wikidata.org/wiki/Q1659609","display_name":"Image warping","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C2779104521","wikidata":"https://www.wikidata.org/wiki/Q23058469","display_name":"Contouring","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C113238511","wikidata":"https://www.wikidata.org/wiki/Q1071612","display_name":"k-nearest neighbors algorithm","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.00069","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.00069","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5760471820831299,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Elastic":[0],"distances":[1,58],"like":[2],"dynamic":[3],"time":[4,10,90],"warping":[5],"(DTW)":[6],"are":[7],"central":[8],"to":[9,56,118],"series":[11,91],"machine":[12,92],"learning":[13,93],"because":[14],"they":[15],"compare":[16],"sequences":[17],"under":[18],"local":[19,65,141],"temporal":[20],"misalignment.":[21],"Soft-DTW":[22],"is":[23,70,121,193],"an":[24,109],"adaptation":[25],"of":[26,106],"DTW":[27,85],"that":[28,167],"can":[29],"be":[30],"used":[31],"as":[32,96],"a":[33,46,103,122],"gradient-based":[34],"loss":[35,112,173],"by":[36],"replacing":[37],"the":[38,64,119,136,140,146,196],"hard":[39],"minimum":[40],"in":[41,86,195],"its":[42],"dynamic-programming":[43,137],"recursion":[44,138],"with":[45,113],"smooth":[47,104,123],"relaxation.":[48],"However,":[49],"this":[50],"approach":[51],"does":[52],"not":[53],"directly":[54],"extend":[55],"elastic":[57,110],"whose":[59],"transition":[60,115,142],"costs":[61],"depend":[62],"on":[63,162],"alignment":[66,111,152],"context.":[67],"Move-Split-Merge":[68],"(MSM)":[69],"one":[71],"such":[72,95],"distance:":[73],"it":[74],"uses":[75],"context-aware":[76,114],"split":[77],"and":[78,81,88,98,108,139,158,179,184],"merge":[79],"penalties":[80],"has":[82],"often":[83],"outperformed":[84],"supervised":[87],"unsupervised":[89],"tasks":[94],"classification":[97,186],"clustering.":[99],"We":[100,144],"introduce":[101],"Soft-MSM,":[102],"relaxation":[105],"MSM":[107,171,176],"costs.":[116],"Central":[117],"formulation":[120],"gated":[124],"surrogate":[125],"for":[126],"MSM's":[127],"piecewise":[128],"split/merge":[129],"cost,":[130],"which":[131],"enables":[132],"gradients":[133],"through":[134],"both":[135],"structure.":[143],"derive":[145],"forward":[147],"recursion,":[148,150],"backward":[149],"soft":[151],"matrix,":[153],"closed-form":[154],"gradient,":[155],"limiting":[156],"behaviour,":[157],"divergence-corrected":[159],"formulation.":[160],"Experiments":[161],"112":[163],"UCR":[164],"datasets":[165],"show":[166],"Soft-MSM":[168],"gives":[169],"lower":[170],"barycentre":[172,177],"than":[174,188],"existing":[175],"methods,":[178],"yields":[180],"significantly":[181],"better":[182],"clustering":[183],"nearest-centroid":[185],"performance":[187],"Soft-DTW-based":[189],"alternatives.":[190],"An":[191],"implementation":[192],"available":[194],"open-source":[197],"\\texttt{aeon}":[198],"toolkit.":[199]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-05T00:00:00"}