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A linear algebra approach to OLAP

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Formal Aspects of Computing

Abstract

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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Authors and Affiliations

  1. INRIA, Centre Paris-Rocquencourt, 23 avenue dItalie, CS 81321, 75214, Paris Cedex 13, France

    Hugo Daniel Macedo

  2. High Assurance Software Lab/INESC TEC and University of Minho, Braga, Portugal

    José Nuno Oliveira

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  1. Hugo Daniel Macedo
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  2. José Nuno Oliveira
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Correspondence to Hugo Daniel Macedo.

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Communicated by Eerke Boiten

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Macedo, H.D., Oliveira, J.N. A linear algebra approach to OLAP. Form Asp Comp 27, 283–307 (2015). https://doi.org/10.1007/s00165-014-0316-9

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  • DOI: https://doi.org/10.1007/s00165-014-0316-9

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