OLAP cube

The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three.

For example, a company might wish to summarize financial data by product, by time-period, and by city to compare actual and budget expenses.

Each cell of the cube holds a number that represents some measure of the business, such as sales, profits, expenses, budget and forecast.

The elements of a dimension can be organized as a hierarchy,[4] a set of parent-child relationships, typically where a parent member summarizes its children.

Conceiving data as a cube with hierarchical dimensions leads to conceptually straightforward operations to facilitate analysis.

[5] The picture shows a drill-down operation: The analyst moves from the summary category "Outdoor protective equipment" to see the sales figures for the individual products.

The summarization rule might be an aggregate function, such as computing totals along a hierarchy or applying a set of formulas such as "profit = sales - expenses".

Insofar as two-dimensional output devices cannot readily characterize three dimensions, it is more practical to project "slices" of the data cube (we say project in the classic vector analytic sense of dimensional reduction, not in the SQL sense, although the two are conceptually similar), which may suppress a primary key, but still have some semantic significance, perhaps a slice of the triadic functional representation for a given Z value of interest.

The motivation[9] behind OLAP displays harks back to the cross-tabbed report paradigm of 1980s DBMS, and to earlier contingency tables from 1904.