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Tensor Approximation for Multidimensional and Multivariate Data

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dc.contributor.authorPajarola, Renato
dc.contributor.authorSuter, Susanne
dc.contributor.authorYang, Haiyang
dc.contributor.authorBallester, Rafael
dc.contributor.funderSeventh Framework Programme
dc.contributor.funderSwiss National Science Foundation
dc.contributor.rorhttps://ror.org/02jjdwm75
dc.date.accessioned2024-07-08T13:15:40Z
dc.date.available2024-07-08T13:15:40Z
dc.date.issued2021
dc.description.abstractTensor decomposition methods and multilinear algebra are powerful tools to cope with challenges around multidimensional and multivariate data in computer graphics,image processing and data visualization,in particular with respect to compact representation and processing of increasingly large-scale data sets. Initially proposed as an extension of the concept of matrix rank for 3 and more dimensions,tensor decomposition methods have found applications in a remarkably wide range of disciplines. We briefly review the main concepts of tensor decompositions and their application to multidimensional visual data. Furthermore,we will include a first outlook on porting these techniques to multivariate data such as vector and tensor fields.
dc.description.fundingtypeAcknowledgements This work was partially supported by the University of Zurich’s Forschungskredit “Candoc” (grant numbers FK-16-012 and 53511401) a Swiss National Science Foundation grant (SNF) (project nº200021_132521) la Hasler Foundation grant (project number 12097) and the EU FP7 People Programme (Marie Curie Actions) under REA Grant Agreement n?290227. Furthermore, we would like to acknowledge the Computer-Assisted Paleoanthropology group and the Visualization and MultiMedia Lab at University of Zürich for the acquisition of the Hazelnut dataset (https://www.ifi.uzh.ch/en/vmml/research/datasets.html in Fig. 15. Also we acknowledge the Johns Hopkins Turbulence Database http://turbulence.pha.jhu.edu/ for the data used in Fig. 16 as well as their forced MHD simulation data http://turbulence.pha.jhu.edu/Forced_ MHD_turbulence.aspx used in our experiments.
dc.formatapplication/pdf
dc.identifier.citationPajarola, R., Suter, S. K., Ballester-Ripoll, R., & Yang, H. (2021). Tensor approximation for multidimensional and multivariate data. In Anisotropy Across Fields and Scales (pp. 73-98). Springer International Publishing.
dc.identifier.doihttps://doi.org/10.1007/978-3-030-56215-1_4
dc.identifier.isbn9783030562144
dc.identifier.issn16123786
dc.identifier.officialurlhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85102587385&doi=10.1007%2f978-3-030-56215-1_4&partnerID=40&md5=35ff9f462672b3644b0372c8a14fb4a2
dc.identifier.publicationtitleAnisotropy Across Fields and Scales
dc.identifier.urihttps://hdl.handle.net/20.500.14417/3193
dc.journal.titleMathematics and Visualization
dc.language.isoeng
dc.page.final98
dc.page.initial73
dc.page.total12
dc.publisherSpringer Science and Business Media Deutschland GmbH
dc.relation.departmentSci Tech (Data Science)
dc.relation.entityIE University
dc.relation.projectIDREA: 290227
dc.relation.projectID SNF: 200021_132521
dc.relation.schoolIE School of Science & Technology
dc.rightsAttribution 4,0 International
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.otherAnisotropy
dc.subject.otherData visualization
dc.subject.otherImage processing
dc.subject.otherTensors
dc.subject.otherVisualization
dc.subject.otherCompact representation
dc.subject.otherLarge scale data sets
dc.subject.otherMatrix rank
dc.subject.otherMulti-linear algebras
dc.subject.otherMultivariate data
dc.subject.otherTensor approximation
dc.subject.otherTensor decomposition
dc.subject.otherTensor fields
dc.subject.otherData handling
dc.titleTensor Approximation for Multidimensional and Multivariate Data
dc.typeinfo:eu-repo/semantics/conferenceObject
dc.version.typeinfo:eu-repo/semantics/publishedVersion
dspace.entity.typePublication
person.identifier.scopus-author-id6701624951
person.identifier.scopus-author-id55017879400
person.identifier.scopus-author-id55813449900
person.identifier.scopus-author-id57222390117
relation.isAuthorOfPublication6f756541-9eb4-430c-9664-1833c080ce57
relation.isAuthorOfPublication.latestForDiscovery6f756541-9eb4-430c-9664-1833c080ce57
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