A linear algebra approach to OLAP-Reference-Cited by-同舟云学术

A linear algebra approach to OLAP

Published:2015-03 Issue:2 Volume:27 Page:283-307
ISSN:0934-5043
Container-title:Formal Aspects of Computing
language:en
Short-container-title:Form. Asp. Comput.

Author:

Macedo Hugo Daniel¹,Oliveira José Nuno²

Affiliation:

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

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

Abstract

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Theoretical Computer Science,Software

Link

http://link.springer.com/content/pdf/10.1007/s00165-014-0316-9.pdf

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