A linear algebra approach to OLAP

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 o...

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Veröffentlicht in:Formal aspects of computing 2015-03, Vol.27 (2), p.283-307
Hauptverfasser: Macedo, Hugo Daniel, Oliveira, José Nuno
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-014-0316-9