The data cube as a typed linear algebra operator

Abstract

There is a need for a typed notation for linear algebra applicable to the ields of econometrics and data mining. In this paper we show that such a notation exists and can be useful in formalizing and reasoning about data aggregation operations. One such operation - the construction of a data cube - is shown to be easily expressible as a linear algebra operator. The construction is shown to be type-generic and some of its properties are derived from its typed deinition and proved using matrix algebra. Other forms of data aggregation such as eg. rollup and cross tabulation are shown to be algebraically derivable from data cubes. © 2017 Association for Computing Machinery.