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A linear algebra approach to OLAP

Bibliographic Details
Main Author: Macedo,HD
Publication Date: 2015
Other Authors: José Nuno Oliveira
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://repositorio.inesctec.pt/handle/123456789/6594
http://dx.doi.org/10.1007/s00165-014-0316-9
Summary: Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.
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spelling A linear algebra approach to OLAPInspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.2018-01-17T10:06:32Z2015-01-01T00:00:00Z2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/6594http://dx.doi.org/10.1007/s00165-014-0316-9engMacedo,HDJosé Nuno Oliveirainfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-10-12T02:22:02Zoai:repositorio.inesctec.pt:123456789/6594Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T18:58:03.208676Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv A linear algebra approach to OLAP
title A linear algebra approach to OLAP
spellingShingle A linear algebra approach to OLAP
Macedo,HD
title_short A linear algebra approach to OLAP
title_full A linear algebra approach to OLAP
title_fullStr A linear algebra approach to OLAP
title_full_unstemmed A linear algebra approach to OLAP
title_sort A linear algebra approach to OLAP
author Macedo,HD
author_facet Macedo,HD
José Nuno Oliveira
author_role author
author2 José Nuno Oliveira
author2_role author
dc.contributor.author.fl_str_mv Macedo,HD
José Nuno Oliveira
description Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.
publishDate 2015
dc.date.none.fl_str_mv 2015-01-01T00:00:00Z
2015
2018-01-17T10:06:32Z
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dc.identifier.uri.fl_str_mv http://repositorio.inesctec.pt/handle/123456789/6594
http://dx.doi.org/10.1007/s00165-014-0316-9
url http://repositorio.inesctec.pt/handle/123456789/6594
http://dx.doi.org/10.1007/s00165-014-0316-9
dc.language.iso.fl_str_mv eng
language eng
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dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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