A Model-Driven Heuristic Approach for
Detecting Multidimensional Facts in Relational
Andrea Carm` e1, Jose-Norberto Maz´ on2, and Stefano Rizzi3
2Lucentia Research Group
Dept. of Software and Computing Systems
University of Alicante, Spain
3DEIS - University of Bologna, Italy
Abstract. Facts are multidimensional concepts of primary interests for
knowledge workers because they are related to events occurring dynam-
ically in an organization. Normally, these concepts are modeled in oper-
ational data sources as tables. Thus, one of the main steps in conceptual
design of a data warehouse is to detect the tables that model facts.
However, this task may require a high level of expertise in the appli-
cation domain, and is often tedious and time-consuming for designers.
To overcome these problems, a comprehensive model-driven approach is
presented in this paper to support designers in: (1) obtaining a CWM
model of business-related relational tables, (2) determining which ele-
ments of this model can be considered as facts, and (3) deriving their
counterparts in a multidimensional schema. Several heuristics –based on
structural information derived from data sources– have been defined to
this end and included in a set of Query/View/Transformation model
The development of data warehouses is based on detecting multidimensional
elements from a detailed analysis of data sources. Among multidimensional el-
ements, facts are those of highest importance since they represent events of
interests for knowledge workers. Therefore, several techniques, such as guide-
lines or glossaries, have been developed so far to support designers in detecting
multidimensional roles of elements in a relational schema (including facts). For
example, in a retail domain, a table called Sales is likely to cover the role of a
fact. However, these techniques may become tedious and time-consuming when
the application domain is complex (in a medical domain, is a table called Fertil-
ityCycle a fact?) or, even worse, when table names are meaningless (what is the
multidimensional counterpart of a table called SP CCCM?).
T.B. Pedersen, M.K. Mohania, and A M. Tjoa (Eds.): DaWaK 2010, LNCS 6263, pp. 13–24, 2010.
c ? Springer-Verlag Berlin Heidelberg 2010
14A. Carm` e, J.-N. Maz´ on, and S. Rizzi
Other approaches arose to support designers in tackling this task in a more
automated manner [1,2,3]. However, these are focused on automatically detecting
other multidimensional concepts (such as dimension hierarchies) rather than
facts, so discovering facts still relies on informal techniques. Furthermore, most
approaches assume that data sources are well-documented or documentation can
be easily obtained; unfortunately, this is not generally true , and even if some
documentation exists, it is likely to be out-of-date with respect to the actual
To overcome these drawbacks, in this paper we present an approach for for-
malizing fact detection from relational data sources without requiring additional
documentation. Our approach is based on a set of heuristics, elicited from some
real-world case studies we are working on. These heuristics use some syntactical
information derived from the data sources, thus guiding designers in the detec-
tion of facts independently of their knowledge about the application domain. We
have formalized these heuristics by means of QVT (Query/View/Transformation)
transformations in a model-driven perspective, in such a way that the final multi-
dimensional schemata are derived with a high degree of automation, thus saving
time and costs. Basically, our approach consists of three tasks (see Fig. 1): (1)
detect clusters of business-related tables within data sources and derive their
relational CWM model, (2) support designers in properly determining which
elements of this model can be considered as facts by means of a set of heuristics-
based QVT model transformations, and (3) model facts, together with their
dimensions and measures, in a multidimensional schema.
The remainder of this paper is structured as follows. Section 2 briefly de-
scribes the current approaches for discovering multidimensional facts. Section 3
describes our heuristics and the definition of model transformations for detect-
ing facts. Section 4 presents an implementation of our approach and draws the
Fig.1. Overview of our approach for detecting facts
A Model-Driven Heuristic Approach for Detecting Multidimensional Facts15
Most approaches for deriving multidimensional schemata from relational data
sources (e.g., [5,6,7,8]) propose informal mechanisms (such as guidelines or glos-
saries) to support designers. In order to increase the level of automation of this
task, other approaches use heuristics to determine which tables are good can-
didates to become facts. Phipps and Davis  propose to consider every entity
in an Entity-Relationship schema that contains numerical attributes as a fact,
which may be unfeasible since (1) most entities in a schema would be selected,
and (2) it is assumed that an up-to-date conceptual schema of data sources is
available. Jensen et al.  consider not only the presence of measures, but also
table cardinality to identify facts; though this approach builds on a reverse-
engineering stage in which relational metadata is obtained from data sources,
its success highly depends on the skill of domain experts.
Two automated approaches for detecting facts are presented in  and .
Song et al.  propose structural heuristics to detect facts from an Entity-
Relationship schema: all entities with a high number of many-to-one relation-
ships are candidates to become facts. Not realistically, they assume that a con-
ceptual schema is always available. Romero and Abell´ o  detect facts by ex-
pressing multidimensional SQL queries over relational data sources, and assume
that those aggregated attributes in the SELECT clause which are not included
in the GROUP BY clause belong to a table that is a potential fact. However, this
approach depends on the ability of the users to express their own information
requirements as SQL queries.
Our work is inspired by , that considers relational data sources as legacy
systems whose documentation either is not available, or cannot be obtained, or
is too complex to be easily understood through a manual analysis. To overcome
these problems, they consider the development of a data warehouse as a modern-
ization scenario which addresses the analysis of the available data sources aimed
at discovering multidimensional structures. These structures are then used to
derive a data-driven multidimensional schema or reconcile a requirement-driven
multidimensional schema with data sources. However, the heuristics for detecting
facts presented in that work are rather simplistic and deliver a single solution,
which may hide the analysis potential of data sources.
3 Model-Driven Heuristic Approach for Detecting Facts
Our model-driven approach aims to support designers in marking tables from
relational data sources as facts. Each table can be differently marked, thus sug-
gesting several possibilities to designers. A set of heuristics for determining
which tables are good candidates for being facts, mainly based on an analy-
sis of functional dependencies, have been developed and formalized by using
QVT (Query/View/Transformation)  model transformations. Our approach
assumes that all database constraints (primary and foreign keys) are known,
which is perfectly reasonable since these constraints can be nimbly derived .
16A. Carm` e, J.-N. Maz´ on, and S. Rizzi
Fig.2. Relational schema for the running example
The example we will use throughout the paper is based on the retail domain
(see Fig. 2) and summarizes situations we have detected in a real case study
we are working on at the Spanish fertility institute TAHE Fertilidad1, which we
cannot show due to confidentiality issues. Data related to sales and orders are
stored, as well as stores, products, etc. Sales are specialized into national and
international ones. The OrderDetail relation allows to include several products
in each order.
3.1Obtaining CWM Models of Data Sources
This phase concerns the extraction of relational elements (tables, columns, and
constraints) from data sources by querying the DBMS data dictionary. It consists
of two steps: (1) delimiting the relational elements related to the application
domain, and (2) creating their models based on CWM.
The rationale behind the first step is that, in real-world scenarios, data sources
not only store interesting data for analysis but also data about instance feed-
ing applications, security, audit, and so on, that should be ignored when facts
are being detected. The benefits of this pre-processing step are twofold: on the
one hand, useless elements are not considered; on the other, heuristics will be
A Model-Driven Heuristic Approach for Detecting Multidimensional Facts 17
more reliable because the required measures will be calculated by considering
only interesting relational elements. Relational elements are first grouped into
clusters, using a graph theory algorithm that computes connected graph com-
ponents . The output is a set of directed, connected graphs whose nodes
and edges represent relations and functional dependencies, respectively. Then
the designer, in collaboration with domain experts, manually determines which
clusters are useful for analysis. In our running example, the cluster containing
table ApplicationAccess is not considered, since it is supposed to be unrelated to
the business domain.
During the second step, a relational CWM (rCWM) model is created for
each selected cluster. Common Warehouse Metamodel (CWM)  consists of
a set of metamodels for representing data warehouse and business intelligence
metadata, including a relational metamodel that allows relational elements to
be easily represented. The next phases of our approach are applied separately
to each rCWM model created. Fig. 3 shows part of the rCWM model for our
Fig.3. Part of the relational CWM model for the running example
The fact detection process (Fig. 4) consists of several steps aimed at (1) marking
relationship cardinalities, (2) calculating the in-degree of tables, (3) marking
facts, (4) marking dimensions and measures, and (5) spawning analysis contexts.
Note that several marks can be applied to each relational element, by adding
18 A. Carm` e, J.-N. Maz´ on, and S. Rizzi
Fig.4. Fact detection process
values to the description attributes provided by CWM. Before explaining the
process steps, we describe the heuristics they rely on.
Heuristics. Our heuristics are based on a set of measures calculated from the
tables of the rCWM model.
1. The first heuristics states that a table may be a fact if it contains a higher
number of instances (NIT) than most other tables. The rationale is that
a large table is frequently updated because it stores data related to dy-
namic events of a business process. The NIT value is retrieved querying
data sources through a simple SQL query.
2. The second heuristics states that a table may be a fact if it has a large ratio
of numerical attributes: NAR = NNA/NTA, where NNA is the number of
numeric attributes and NTA is the total number of attributes of a table.
3. The third heuristics states that a table may be a fact if it has a low in-degree,
i.e., few or no incoming foreign keys (an incoming foreign key for table T is
a foreign key referencing the primary key of T).
To quantify qualitative terms such as “high” and “few”, we computed three
thresholds. Thresholds for NIT and NAR are calculated using the statistical
percentile concept . We have chosen the upper quartile (75-th percentile)
as the NIT threshold and the lower quartile (25-th percentile) as the NAR
threshold because this gave good results in our case study. Of course, further
tests will be needed to find the best percentile to be used in general cases. The
in-degree threshold is fixed to 1, which means considering as potential facts only
tables with one or no incoming foreign key. We use 1 instead of 0 to consider
some specific patterns that we will explain in the following subsections.
Each heuristic measure is stored in a CWM tagged value connected to the
related table, as shown in Fig. 3. Thresholds are stored using tagged values
linked to the package that contains relational elements.
Marking relationship cardinalities. The relational model has a limited
expressiveness. Specifically, one-to-one relationships, that have an ad-hoc rep-
resentation in the Entity-Relationship model, are not explicitly modeled in a
relational schema. Indeed, the existence of a foreign key between two tables does
not explain if the relationship between these tables is many-to-one or one-to-one.
Since this knowledge is necessary for our approach, we use two transformations
to single out two kinds of one-to-one relationships that we will call, respectively,
strong and weak.
A Model-Driven Heuristic Approach for Detecting Multidimensional Facts19
– Strong one-to-one relationships are schema-based since they are derived and
validated within the schema structure. Precisely, a strong one-to-one rela-
tionship between two tables T and S is detected when the primary key of
T is a foreign key referencing S. A QVT transformation checks this pattern
inside rCWM models and marks the foreign keys involved as one-to-one.
– Weak one-to-one relationships are instance-based, since they are elicited from
data sources instances. A weak one-to-one relationship between T and S is
detected when T includes a foreign key (different from its primary key)
referencing S, and at most one tuple of T has the value of the primary
key of each tuple of S. In this case, no explicit schema constraint assured
the correctness of this cardinality assumption; however, considering that
data warehouse systems are typically fed by data sources populated with a
huge amount of data –hence, instances are representative of the application
domain–, we can reasonably take it as true. A specific QVT transformation
has been developed for detecting this pattern by integrating the algorithm
proposed in . Precisely, two queries are performed over T to count the
number of non-null values of its foreign key with and without duplicates;
the QVT transformation stores the results, compares them, and marks the
foreign key as one-to-one if they are equal.
Foreign keys not marked as one-to-one are marked as many-to-one. In our run-
ning example, the foreign keys that link NationalSale and InternationalSale to
Sale are marked as (strong) one-to-one, as well as the (weak) one that connects
Organizer to Category. The other foreign keys are marked as many-to-one.
Calculating the in-degree of tables. A QVT transformation rule has been
defined to calculate in-degree of tables. Note that a foreign key that has already
been marked as one-to-one is not taken into account here, due to the possibility
to navigate these relationships in both ways. Indeed, two tables marked as facts
can be linked by a foreign key expressing a one-to-one relationship.
In our running example, table Order has in-degree 1, while Sale has in-degree 0
even if it has two incoming foreign keys (from NationalSale and InternationalSale,
respectively), because these were marked as one-to-one.
Marking facts and measures. A table is marked as a fact if (1) its NIT and
NAR are greater or equal to the thresholds, and (2) its in-degree is 0 or 1. The
comparison is made by the QVT transformation presented in Fig. 5. Then, all
numerical attributes of each table T marked as fact (excluding those belonging
to the primary key of T) are marked as potential measures. In our example, Sale,
Order, OrderDetail, and Product meet the first constraint, so they can be marked
as facts. However, Product is not marked as a fact because its in-degree is 2 (i.e.
the second constraint is not fulfilled).
Marking dimensions. For each table T marked as fact, its dimensions and
the related hierarchies can be derived by following many-to-one relationships as
normally done in current approaches (e.g., [5,1]).
20A. Carm` e, J.-N. Maz´ on, and S. Rizzi
Fig.5. QVT transformation for marking facts
Spawning analysis contexts. The aim of this phase is to create a set of
models, each related to a possible analysis context, so as to generate every mul-
tidimensional solution implicitly contained in the relational data sources. This
is done in two situations:
1. Fact-dimension conflicts. After the marking process, the marked rCWM
model may present some configurations of marks that lead to inconsistencies
in the multidimensional schema. These conflicts must be handled before cre-
ating the multidimensional representation of elements. Precisely, a marked
rCWM model contains a conflict when a table is marked both as a fact and
as a dimension. In our example, there is a conflict in the Order table. To
overcome this problem, for each table T that has a conflict two rCWM mod-
els, corresponding to two different analysis contexts, are spawned: one where
T is marked as dimension, one where it is marked as fact.
2. Specialization. When a table T marked as fact has a one-to-one foreign key
referencing table S, we spawn two rCWM models: only S is marked as fact
in the first one; S and T are marked as facts in the second one. For example,
InternationalSale and NationalSale are both linked with one-to-one relation-
ships to Sale. This leads to creating three rCWM models where: (1) only Sale
is marked as fact, (2) Sale and InternationalSale are marked as facts, and (3)
Sale and NationalSale are marked as facts.
In the end, the total number of rCWM models spawned depends on the number
of conflicts and specializations in the original marked rCWM model. Precisely,
the total number of rCWM models is MN = (CN ∗ 2) ∗?SN
SNTithe number of tables involved in the i-th specialization.
It is worth noting that an exponential number of rCWM models is obtained
this way. In order to manage these high amount of models, our proposal can be
easily integrated in the model-driven approach for data warehouse development
proposed in [16,17], where the rCWM models can be reconciled with a conceptual
is the number of fact-dimension conflicts, SN the number of specializations, and
A Model-Driven Heuristic Approach for Detecting Multidimensional Facts 21
schema previously defined from the information requirements of decision makers.
A single multidimensional schema, that at the same time fits data sources and
fulfills user requirements, is obtained this way. Due to space constraints, this
reconciliation phase is not discussed in this paper.
3.3 Deriving Multidimensional Elements
The spawning phase creates one or more rCWM models. Two special patterns
have been developed for handling special situations that can arise afterwards,
namely (1) skip and (2) merge. Both share the same starting situation, i.e., two
tables T and S marked as facts and such that T references S via a foreign key.
The patterns are distinguished depending on the the mark applied to this foreign
1. When the foreign key is marked as many-to-one, a skip pattern is detected.
In this case, T and its dimensions are not included in the multidimensional
schema, so as to focus on the right granularity in each case. For example,
the OrderDetail fact-marked table is skipped and Order is considered as fact.
We recall that OrderDetail will be considered as fact in one or more other
2. A merge pattern is detected when the foreign key is marked as one-to-one.
In this case, a fact is created whose dimensions and measures are the union
of those belonging to T and S. For instance, Sale can be merged with Na-
tionalSale or InternationalSale to create facts for national and international
analysis purposes, respectively.
These patterns are applied using QVT transformations, one of which
(Table2Merge) is shown in Fig. 6b. In this merge transformation, an input pat-
tern consisting of a table T marked as fact that refers S by means of a foreign
key fk marked as one-to-one, leads to create a fact f (previously created from
table S by means of the Table2MDFact transformation as shown in Fig. 6a). Im-
portantly, according to the QVT transformations called in the WHERE clause,
(a) Obtaining facts
(b) Merging facts
Fig.6. QVT from a marked rCWM model to a multidimensional schema
22A. Carm` e, J.-N. Maz´ on, and S. Rizzi
Fig.7. Transformation execution order
Fig.8. Approach results over running example
the multidimensional counterparts of all the tables related to T will be related
to f. Besides, when merge transformations are applied, the name of the table
analyzed in the last merge transformation called is chosen as the fact name.
As to the order for applying transformations, the Table2MDFact transforma-
tion is executed first to create all facts, then special patterns are detected and
applied by means of the QVT transformations called in the WHERE clause.
The transformation flow is graphically represented in Fig. 7 using the approach
defined in .
In Fig. 8 we present the solutions derived by applying our approach to the
running example (measures and time dimensions are not shown for simplicity).
The solutions in Fig. 8a, 8b, and 8c consider as facts OrderDetail and Sale in a
A Model-Driven Heuristic Approach for Detecting Multidimensional Facts23
general, national, and international analysis context respectively. The solutions
in Fig. 8d, 8e, and 8f consider as facts Order rather than OrderDetail. As a whole,
these solutions bring to light the full multidimensional potential of data sources;
designers can then select the solution that best matches user requirements.
4 Conclusions and Future Work
Current approaches for data-driven conceptual design do not give designers a
comprehensive and formal approach to detect facts. To fill this gap, in this
paper we presented a model-driven approach for formalizing fact discovery in re-
lational data sources by means of QVT transformations. Our approach is based
on a set of heuristics relying on syntactical information derived from the data
sources, thus guiding designers in the detection of multidimensional facts inde-
pendently of their knowledge about the application domain. Remarkably, our
approach has low computational complexity; the total processing time for the
largest relational source schema we used for testing (about 130 tables and 140
foreign key constraints) is about 20 seconds.
The proposed model transformations have been implemented in the Eclipse2
development platform. Eclipse is an open source project which has been con-
ceived as a modular platform that can be extended by means of plugins in order
to add more features and new functionalities. In that way, we have designed
a set of modules encapsulated in a single plugin that provides Eclipse with
capabilities for supporting our approach:
Relational module. ItimplementstherelationalmetamodelcontainedinCWM.
Multidimensional module. The profiling mechanism of the Unified Modeling
Language (UML) has been used to create multidimensional models.
Transformation module. It uses mediniQVT3, a QVT transformation en-
gine, in order to code and execute the mapping patterns.
Acknowledgments. This work has been supported by the QUASIMODO
(PAC08-0157-0668) project from the Castilla-La Mancha Ministry of Educa-
tion and Science (Spain). We would like to express our gratitude to personnel at
TAHE Fertilidad (http://www.tahefertilidad.es) for their support during
the development of this work.
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