An OLAP cube is an array of data understood in terms of its 0 or more dimensions.
OLAP is an acronym for online analytical processing.
OLAP is a computer-based technique for analyzing business data in the search for business intelligence.
Terminology A cube can be considered a generalization
of a three-dimensional spreadsheet.
For example, a company might wish to summarize financial data by product, by time-period,
and by city to compare actual and budget expenses.
Product, time, city and scenario are the data's dimensions.
Cube is a shortcut for multidimensional dataset, given that data can have an arbitrary number
of dimensions.
The term hypercube is sometimes used, especially for data with more than three dimensions.
Slicer is a term for a dimension which is held constant for all cells so that multidimensional
information can be shown in a two dimensional physical space of a spreadsheet or pivot table.
Each cell of the cube holds a number that represents some measure of the business, such
as sales, profits, expenses, budget and forecast.
OLAP data is typically stored in a star schema or snowflake schema in a relational data warehouse
or in a special-purpose data management system.
Measures are derived from the records in the fact table and dimensions are derived from
the dimension tables.
Hierarchy The elements of a dimension can be organized
as a hierarchy, a set of parent-child relationships, typically where a parent member summarizes
its children.
Parent elements can further be aggregated as the children of another parent.
For example May 2005's parent is Second Quarter 2005 which is in turn the child of Year 2005.
Similarly cities are the children of regions; products roll into product groups and individual
expense items into types of expenditure.
Operations Conceiving data as a cube with hierarchical
dimensions leads to conceptually straightforward operations to facilitate analysis.
Aligning the data content with a familiar visualization enhances analyst learning and
productivity.
The user-initiated process of navigating by calling for page displays interactively, through
the specification of slices via rotations and drill down/up is sometimes called "slice
and dice".
Common operations include slice and dice, drill down, roll up, and pivot.
Slice is the act of picking a rectangular subset of a cube by choosing a single value
for one of its dimensions, creating a new cube with one fewer dimension.
The picture shows a slicing operation: The sales figures of all sales regions and all
product categories of the company in the year 2004 are "sliced" out of the data cube.
Dice: The dice operation produces a subcube by allowing the analyst to pick specific values
of multiple dimensions.
The picture shows a dicing operation: The new cube shows the sales figures of a limited
number of product categories, the time and region dimensions cover the same range as
before.
Drill Down/Up allows the user to navigate among levels of data ranging from the most
summarized to the most detailed.
The picture shows a drill-down operation: The analyst moves from the summary category
"Outdoor-Schutzausrüstung" to see the sales figures for the individual products.
Roll-up: A roll-up involves summarizing the data along a dimension.
The summarization rule might be computing totals along a hierarchy or applying a set
of formulas such as "profit = sales - expenses".
Pivot allows an analyst to rotate the cube in space to see its various faces.
For example, cities could be arranged vertically and products horizontally while viewing data
for a particular quarter.
Pivoting could replace products with time periods to see data across time for a single
product.
The picture shows a pivoting operation: The whole cube is rotated, giving another perspective
on the data.
Mathematical definition In database theory, an OLAP cube is an abstract
representation of a projection of an RDBMS relation.
Given a relation of order N, consider a projection that subtends X, Y, and Z as the key and W
as the residual attribute.
Characterizing this as a function, f : → W,
the attributes X, Y, and Z correspond to the axes of the cube, while the W value into which
each triple maps corresponds to the data element that populates each cell of the cube.
Insofar as two-dimensional output devices cannot readily characterize three dimensions,
it is more practical to project "slices" of the data cube,
g : → W 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 behind OLAP displays harks back to the cross-tabbed report paradigm of
1980s DBMS.
The resulting spreadsheet-style display, where values of X populate row $1; values of Y populate
column $A; and values of g : → W populate the individual cells "southeast of" $B2, so
to speak, $B2 itself included.
See also
References
External links Daniel Lemire.
"Data Warehousing and OLAP - A Research-Oriented Bibliography".
Retrieved 2008-03-05.
The RDF Data Cube Vocabulary