Zobrazit minimální záznam

dc.contributor.authorSnášel, Václav
dc.contributor.authorNowaková, Jana
dc.contributor.authorXhafa, Fatos
dc.contributor.authorBarolli, Leonard
dc.date.accessioned2017-01-05T12:35:05Z
dc.date.available2017-01-05T12:35:05Z
dc.date.issued2017
dc.identifier.citationFuture Generation Computer Systems. 2017, vol. 67, p. 286-296.cs
dc.identifier.issn0167-739X
dc.identifier.issn1872-7115
dc.identifier.urihttp://hdl.handle.net/10084/116567
dc.description.abstractModern data science uses topological methods to find the structural features of data sets before further supervised or unsupervised analysis. Geometry and topology are very natural tools for analysing massive amounts of data since geometry can be regarded as the study of distance functions. Mathematical formalism, which has been developed for incorporating geometric and topological techniques, deals with point cloud data sets, i.e. finite sets of points. It then adapts tools from the various branches of geometry and topology for the study of point cloud data sets. The point clouds are finite samples taken from a geometric object, perhaps with noise. Topology provides a formal language for qualitative mathematics, whereas geometry is mainly quantitative. Thus, in topology, we study the relationships of proximity or nearness, without using distances. A map between topological spaces is called continuous if it preserves the nearness structures. Geometrical and topological methods are tools allowing us to analyse highly complex data. These methods create a summary or compressed representation of all of the data features to help to rapidly uncover particular patterns and relationships in data. The idea of constructing summaries of entire domains of attributes involves understanding the relationship between topological and geometric objects constructed from data using various features. A common thread in various approaches for noise removal, model reduction, feasibility reconstruction, and blind source separation, is to replace the original data with a lower dimensional approximate representation obtained via a matrix or multi-directional array factorization or decomposition. Besides those transformations, a significant challenge of feature summarization or subset selection methods for Big Data will be considered by focusing on scalable feature selection. Lower dimensional approximate representation is used for Big Data visualization. The cross-field between topology and Big Data will bring huge opportunities, as well as challenges, to Big Data communities. This survey aims at bringing together state-of-the-art research results on geometrical and topological methods for Big Data.cs
dc.format.extent1185851 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoencs
dc.publisherElseviercs
dc.relation.ispartofseriesFuture Generation Computer Systemscs
dc.relation.urihttp://dx.doi.org/10.1016/j.future.2016.06.005cs
dc.rights© 2016 The Author(s). Published by Elsevier B.V.cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/cs
dc.subjectIndustry 4.0cs
dc.subjectbig datacs
dc.subjecttopological data analysiscs
dc.subjectpersistent homologycs
dc.subjectdimensionality reductioncs
dc.subjectbig data visualizationcs
dc.titleGeometrical and topological approaches to Big Datacs
dc.typearticlecs
dc.identifier.doi10.1016/j.future.2016.06.005
dc.rights.accessopenAccess
dc.type.versionpublishedVersioncs
dc.type.statusPeer-reviewedcs
dc.description.sourceWeb of Sciencecs
dc.description.volume67cs
dc.description.lastpage296cs
dc.description.firstpage286cs
dc.identifier.wos000389555700023


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Zobrazit minimální záznam

© 2016 The Author(s). Published by Elsevier B.V.
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