03-08-2012, 04:12 PM
An Object Oriented Multidimensional Data Model for OLAP
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Abstract.
Online Analytical Processing (OLAP) data is frequently organized in
the form of multidimensional data cubes each of which is used to examine a set
of data values, called measures, associated with multiple dimensions and their
multiple levels. In this paper, we first propose a conceptual multidimensional
data model, which is able to represent and capture natural hierarchical
relationships among members within a dimension as well as the relationships
between dimension members and measure data values. Hereafter, dimensions
and data cubes with their operators are formally introduced. Afterward, we use
UML (Unified Modeling Language) to model the conceptual multidimensional
model in the context of object oriented databases.
Introduction
Data warehouses and OLAP are essential elements of decision support [5], they
enable business decision makers to creatively approach, analyze and understand
business problems [16]. While data warehouses are built to store very large amounts
of integrated data used to assist the decision-making process [9], the concept of
OLAP, which is first formulated in 1993 by [6] to enable business decision makers to
work with data warehouses, supports dynamic synthesis, analysis, and consolidation
of large volumes of multidimensional data [7]. OLAP systems organize data using the
multidimensional paradigm in the form of data cubes, each of which is a combination
of multiple dimensions with multiple levels per dimension. Summarized data is preaggregated
and stored with the main purpose to explore the relationship between
independent, static variables, dimensions, and dependent, dynamic variables,
measures [3]. Moreover, dimensions always have structures and are linguistic
categories that describe different ways of looking at the information [4]. These
dimensions contain one or more natural hierarchies, together with other attributes that
do not have a hierarchy’s relationship to any of the attributes in the dimensions [10].
Related works
Since Codd’s [6] formulated the term Online Analytical Processing (OLAP) in 1993,
many commercial products, like Arborsoft (now Hyperion) Essbase, Cognos
Powerplay or MicroStrategy’s DSS Agent have been introduced on the market [2].
But unfortunately, sound concepts were not available at the time of the commercial
products being developed. The scientific community struggles hard to deliver a
common basis for multidimensional data models ([1], [4], [8], [11], [12], [13], [21]).
The data models presented so far differ in expressive power, complexity and
formalism. In the followings, some research works in the field of data warehousing
systems and OLAP tools are summarized.
In [12] a multidimensional data model is introduced based on relational elements.
Dimensions are modeled as “dimension relations”, practically annotating attributes
with dimension names. The cubes are modeled as functions from the Cartesian
product of the dimensions to the measure and are mapped to “grouping relations”
through an applicability definition.
In [8] n-dimensional tables are defined and a relational mapping is provided
through the notation of completion. Multidimensional database are considered to be
composed from set of tables forming denormalized star schemata. Attribute
hierarchies are modeled through the introduction of functional dependencies in the
attributes of dimension tables.
The Concepts of Dimensions
First, we introduce hierarchical relationships among dimension members by means of
one hierarchical domain per dimension. A hierarchical domain is a set of dimension
members, organized in hierarchy of levels, corresponding to different levels of
granularity. It allows us to consider a dimension schema as a partially ordered set of
levels. In this concept, a hierarchy is a path along the dimension schema, beginning at
the root level and ending at a leaf level. Moreover, the recursive definitions of two
dimension operators, namely ancestor and descendant, provide abilities to navigate
along a dimension structure. In a consequence, dimensions with any complexity in
their structures can be captured with this data model.
The Concepts of Data Cubes
A multidimensional cube is constructed based on a set dimensions and a set of
measures, and consists a collection of cells. Each cell is an intersection among a set of
dimension members and measure data values. Furthermore, cells are grouped into
granular groupbys, each of which expresses a mapping from the domains of x-tuple of
dimension levels (independent variables) to y-numerical domains of y-tuple of
numeric measures (dependent variables).