Data cube

Data Cube:
A Multidimensional
Data Model

Example
• Although we usually think of cubes as 3-D geometric structures, in data
warehousing the data cube is n-dimensional.
• To gain a better understanding of data cubes and the multidimensional
data model, let’s start by looking at a simple 2-D data cube that is, in fact, a
table or spreadsheet for sales data from AllElectronics.
• In particular, we will look at the AllElectronics sales data for items sold per
quarter in the city of Vancouver.
• These data are shown in Table 4.2. In this 2-D representation, the sales for
Vancouver are shown with respect to the time dimension (organized in
quarters) and the item dimension (organized according to the types of
items sold).
• The fact or measure displayed is dollars sold (in thousands).

Example
• Now, suppose that we would like to view the sales data with a third
dimension.
• For instance, suppose we would like to view the data according to
time and item, as well as location, for the cities Chicago, New York,
Toronto, and Vancouver.
• These 3-D data are shown in Table 4.3. The 3-D data in the table are
represented as a series of 2-D tables.
• Conceptually, we may also represent the same data in the form of a 3-
D data cube, as in Figure 4.3.

3-D
In this way, we may display any n-dimensional data as a series of (n-1)-dimensional “cubes.” The data
cube is a metaphor for multidimensional data storage. The actual physical storage of such data may
differ from its logical representation. The important thing to remember is that data cubes are n-
dimensional and do not confine data to 3-D.

4.4 is often referred to as a cuboid

Stars, Snowflakes, and Fact Constellations:
Schemas for Multidimensional Data Models
The most popular data model for a data warehouse is a multidimensional
model, which can exist in the form of a star schema, a snowflake schema, or
a fact constellation schema. Let’s look at each of these.
• Star schema: The most common modeling paradigm is the star schema, in
which the data warehouse contains (1) a large central table (fact table)
containing the bulk of the data, with no redundancy, and (2) a set of
smaller attendant tables (dimension tables), one for each dimension. The
schema graph resembles a starburst, with the dimension tables displayed
in a radial pattern around the central fact table.

Star schema of sales data warehouse

Snowflake schema: The snowflake schema is a variant of the star
schema model, where some dimension tables are normalized, thereby
further splitting the data into additional tables. The resulting schema
graph forms a shape similar to a snowflake.

Snowflake schema of a sales data warehouse

• Fact constellation: Sophisticated applications may require multiple
fact tables to share dimension tables. This kind of schema can be
viewed as a collection of stars, and hence is called a galaxy schema or
a fact constellation.

Fact constellation schema of a sales and shipping
data warehouse

Dimensions: The Role of Concept Hierarchies
• A concept hierarchy defines a sequence of mappings from a set of
low-level concepts to higher-level, more general concepts.
• Consider a concept hierarchy for the dimension location. City values
for location include Vancouver, Toronto, New York, and Chicago.
• Each city, however, can be mapped to the province or state to which it
belongs.
• For example, Vancouver can be mapped to British Columbia, and
Chicago to Illinois.

Hierarchical and lattice structures

A concept hierarchy for price.

Examples of typical OLAP operations on
multidimensional data

A Starnet Query Model for Querying
Multidimensional Databases

Data cube

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