- home
- Advanced Search
Filters
Clear All- Digital Humanities and Cultural Heritage
- Publications
- Research data
- Other research products
- PL
- arXiv.org e-Print Archive
- Digital Humanities and Cultural Heritage
- Publications
- Research data
- Other research products
- PL
- arXiv.org e-Print Archive
Loading
description Publicationkeyboard_double_arrow_right Part of book or chapter of book , Conference object , Article 2016 ItalyPublisher:Springer International Publishing Funded by:EC | GRAVITATE, EC | IQMULUS, EC | TOPOSYSEC| GRAVITATE ,EC| IQMULUS ,EC| TOPOSYSAuthors: Cerri, Andrea; Ethier, Marc; Frosini, Patrizio;Cerri, Andrea; Ethier, Marc; Frosini, Patrizio;handle: 11585/545254
Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines having a positive slope, it has two main drawbacks. First, it forgets the natural link between the homological properties of filtrations associated with lines that are close to each other. As a consequence, part of the interesting homological information is lost. Second, its intrinsically discontinuous definition makes it difficult to study its properties. In this paper we introduce a new matching distance for 2D persistent Betti numbers, called coherent matching distance and based on matchings that change coherently with the filtrations we take into account. Its definition is not trivial, as it must face the presence of monodromy in multidimensional persistence, i.e. the fact that different paths in the space parameterizing the above filtrations can induce different matchings between the associated persistent diagrams. In our paper we prove that the coherent 2D matching distance is well-defined and stable. Comment: 11 pages, 1 figure
http://arxiv.org/pdf... arrow_drop_down arXiv.org e-Print ArchiveOther literature type . Preprint . 2016Data sources: arXiv.org e-Print Archivehttps://doi.org/10.1007/978-3-...Part of book or chapter of book . 2016 . Peer-reviewedLicense: Springer TDMData sources: Crossrefhttps://doi.org/10.48550/arxiv...Article . 2016License: arXiv Non-Exclusive DistributionData sources: Dataciteadd ClaimPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.All Research productsarrow_drop_down <script type="text/javascript"> <!-- document.write('<div id="oa_widget"></div>'); document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/978-3-319-39441-1_20&type=result"></script>'); --> </script>
For further information contact us at helpdesk@openaire.euAccess RoutesGreen 4 citations 4 popularity Average influence Average impulse Average Powered by BIP!more_vert http://arxiv.org/pdf... arrow_drop_down arXiv.org e-Print ArchiveOther literature type . Preprint . 2016Data sources: arXiv.org e-Print Archivehttps://doi.org/10.1007/978-3-...Part of book or chapter of book . 2016 . Peer-reviewedLicense: Springer TDMData sources: Crossrefhttps://doi.org/10.48550/arxiv...Article . 2016License: arXiv Non-Exclusive DistributionData sources: Dataciteadd ClaimPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.All Research productsarrow_drop_down <script type="text/javascript"> <!-- document.write('<div id="oa_widget"></div>'); document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/978-3-319-39441-1_20&type=result"></script>'); --> </script>
For further information contact us at helpdesk@openaire.eu
Loading
description Publicationkeyboard_double_arrow_right Part of book or chapter of book , Conference object , Article 2016 ItalyPublisher:Springer International Publishing Funded by:EC | GRAVITATE, EC | IQMULUS, EC | TOPOSYSEC| GRAVITATE ,EC| IQMULUS ,EC| TOPOSYSAuthors: Cerri, Andrea; Ethier, Marc; Frosini, Patrizio;Cerri, Andrea; Ethier, Marc; Frosini, Patrizio;handle: 11585/545254
Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines having a positive slope, it has two main drawbacks. First, it forgets the natural link between the homological properties of filtrations associated with lines that are close to each other. As a consequence, part of the interesting homological information is lost. Second, its intrinsically discontinuous definition makes it difficult to study its properties. In this paper we introduce a new matching distance for 2D persistent Betti numbers, called coherent matching distance and based on matchings that change coherently with the filtrations we take into account. Its definition is not trivial, as it must face the presence of monodromy in multidimensional persistence, i.e. the fact that different paths in the space parameterizing the above filtrations can induce different matchings between the associated persistent diagrams. In our paper we prove that the coherent 2D matching distance is well-defined and stable. Comment: 11 pages, 1 figure
http://arxiv.org/pdf... arrow_drop_down arXiv.org e-Print ArchiveOther literature type . Preprint . 2016Data sources: arXiv.org e-Print Archivehttps://doi.org/10.1007/978-3-...Part of book or chapter of book . 2016 . Peer-reviewedLicense: Springer TDMData sources: Crossrefhttps://doi.org/10.48550/arxiv...Article . 2016License: arXiv Non-Exclusive DistributionData sources: Dataciteadd ClaimPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.All Research productsarrow_drop_down <script type="text/javascript"> <!-- document.write('<div id="oa_widget"></div>'); document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/978-3-319-39441-1_20&type=result"></script>'); --> </script>
For further information contact us at helpdesk@openaire.euAccess RoutesGreen 4 citations 4 popularity Average influence Average impulse Average Powered by BIP!more_vert http://arxiv.org/pdf... arrow_drop_down arXiv.org e-Print ArchiveOther literature type . Preprint . 2016Data sources: arXiv.org e-Print Archivehttps://doi.org/10.1007/978-3-...Part of book or chapter of book . 2016 . Peer-reviewedLicense: Springer TDMData sources: Crossrefhttps://doi.org/10.48550/arxiv...Article . 2016License: arXiv Non-Exclusive DistributionData sources: Dataciteadd ClaimPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.This Research product is the result of merged Research products in OpenAIRE.
You have already added works in your ORCID record related to the merged Research product.All Research productsarrow_drop_down <script type="text/javascript"> <!-- document.write('<div id="oa_widget"></div>'); document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/978-3-319-39441-1_20&type=result"></script>'); --> </script>
For further information contact us at helpdesk@openaire.eu