On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems

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dc.contributor.authorHarár, Pavolcs
dc.coverage.issue3cs
dc.coverage.volume62cs
dc.date.issued2020-08-23cs
dc.description.abstractThe use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy.en
dc.formattextcs
dc.format.extent376-394cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of Mathematical Imaging and Vision. 2020, vol. 62, issue 3, p. 376-394.en
dc.identifier.doi10.1007/s10851-019-00902-2cs
dc.identifier.issn1573-7683cs
dc.identifier.orcid0000-0001-5206-1794cs
dc.identifier.other158172cs
dc.identifier.urihttp://hdl.handle.net/11012/187007
dc.language.isoencs
dc.publisherSpringercs
dc.relation.ispartofJournal of Mathematical Imaging and Visioncs
dc.relation.urihttps://link.springer.com/article/10.1007/s10851-019-00902-2cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1573-7683/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectorthogonal projectionsen
dc.subjectdimension reductionen
dc.subjectaugmented target lossen
dc.titleOn Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problemsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-158172en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:42:04en
sync.item.modts2025.01.17 15:24:20en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav telekomunikacícs
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