MRE-KDD+: A MULTI-RESOLUTION, ENSEMBLE-BASED
MODEL FOR ADVANCED KNOLWEDGE DISCOVERY
Alfredo Cuzzocrea
Department of Electronics, Computer Science, and Systems
University of Calabria, Italy
Keywords: On-Line Analytical Processing, Data Mining, On-Line Analytical Mining, Knowledge Discovery from
Large Databases and Data Warehouses, Cooperative Information Systems.
Abstract: In data-intensive scenarios, data repositories expose very different formats, and knowledge representation
schemes are very heterogeneous accordingly. As a consequence, a relevant research challenge is how to
efficiently integrate, process and mine such distributed knowledge in order to make available it to end-
users/applications in an integrated and summarized manner. Starting from these considerations, in this paper
we propose an OLAM-based model for advanced knowledge discovery, called Multi-Resolution Ensemble-
based Model for Advanced Knowledge Discovery in Large Databases and Data Warehouses (MRE-KDD
+
).
MRE-KDD
+
integrates in a meaningfully manner several theoretical amenities coming from On-Line
Analytical Processing (OLAP), Data Mining (DM) and Knowledge Discovery in Databases (KDD), and
results to be an effective model for supporting advanced decision-support processes in many fields of real-
life data-intensive applications.
1 INTRODUCTION
In data-intensive scenarios, intelligent applications
run on top of enormous-in-size, heterogeneous data
sources in order to implement advanced decision-
support processes. Data sources range from
transactional data to XML data, and from workflow-
process log-data to sensor network data; here,
collected data are typically represented, stored and
queried in large databases and data warehouses,
which, without any loss of generality, define a
collection of distributed and heterogeneous data
sources, each of them executing as a singleton
software component (e.g., DBMS server, DW
server, XDBMS server etc). Contrarily to this so-
delineated distributed setting, intelligent applications
wish to extract integrated, summarized knowledge
from such data sources, in order to make strategic
decisions for their business. Nevertheless,
heterogeneity of data and platforms, and distribution
of architectures and systems represent a serious
limitation for the achievement of this goal. As a
consequence, research communities have devoted a
great deal of attention to this problem, with a wide
set of proposals (Fayyad et al., 1996) ranging from
Data Mining (DM) tools, which concern algorithms
for extracting patterns and regularities from data, to
Knowledge Discovery in Databases (KDD)
techniques, which concern the overall process of
discovering useful knowledge from data.
Among the plethora of techniques proposed in
literature to overcome the above-highlighted gap
between data and knowledge, On-Line Analytical
Mining (OLAM) (Han, 1997) is a successful
solution that integrates On-Line Analytical
Processing (OLAP) (Gray et al., 1997) with DM in
order to provide an integrated methodology for
extracting useful knowledge from large databases
and data warehouses. The benefits of OLAM have
been already put-in-evidence (Han, 1997): (i) DM
algorithms can execute on integrated, OLAP-based
multidimensional views that are already pre-
processed and cleaned; (ii) users/applications can
take advantages from the interactive, exploratory
nature of OLAP tools to decisively enhance the
knowledge fruition experience; (iii)
users/applications can take advantages from the
flexibility of OLAP tools in making available a wide
set of DM solutions for a given KDD task, so that,
thanks to OLAP, different DM algorithms become
easily interchangeable in order to decisively
enhance the benefits coming from cross-comparative
152
Cuzzocrea A. (2007).
MRE-KDD+: A MULTI-RESOLUTION, ENSEMBLE-BASED MODEL FOR ADVANCED KNOLWEDGE DISCOVERY.
In Proceedings of the Ninth International Conference on Enterprise Information Systems - AIDSS, pages 152-158
DOI: 10.5220/0002404001520158
Copyright
c
 SciTePress

data analysis methodologies over large amounts of
data.
Starting from these considerations, in this paper
we propose an OLAM-based framework for
advanced knowledge discovery, along with a formal
model underlying this framework, called Multi-
Resolution Ensemble-based Model for Advanced
Knowledge Discovery in Large Databases and
Data Warehouses (MRE-KDD
+
). On the basis of
OLAP principles, MRE-KDD
+
, which can be
reasonably considered as an innovative contribution
in this research field, provides a formal, rigorous
methodology for implementing advanced KDD
processes in data-intensive settings, but with
particular regard to two specialized instances
represented by (i) a general application scenario
populated by distributed and heterogeneous data
sources, such as a conventional distributed data
warehousing environment (e.g., like those that one
can find in B2B and B2C e-commerce systems), and
(ii) the integration/data layer of cooperative
information systems, where different data sources
are integrated in a unique middleware in order to
make KDD processes against these data sources
transparent-to-the-user.
Besides the widely-accepted benefits coming
from integrating OLAM within its core layer (Han,
1997), MRE-KDD
+
allows data-intensive
applications adhering to the methodology it defines
to take advantages from other relevant
characteristics, among which we recall the
following: (i) the multi-resolution support offered by
popular OLAP operators/tools (Han & Kamber,
2000), which allow us to execute DM algorithms
over integrated and summarized multidimensional
views of data at different level of granularity and
perspective of analysis, thus sensitively improving
the quality of KDD processes; (ii) the ensemble-
based support, which, briefly, consists in
meaningfully combining results coming from
different DM algorithms executed over a collection
of multidimensional views in order to generate the
final knowledge, and provide facilities at the
knowledge fruition layer.
The remaining part of this paper is organized as
follows. In Section 2, we outline related work. In
Section 3, we present in detail MRE-KDD
+
.
Finally, in Section 4 we outline conclusions of our
work, and further activities in this research field.
2 RELATED WORK
OLAM is a powerful technology for supporting
knowledge discovery from large databases and data
warehouses that mixes together OLAP
functionalities for representing/processing data, and
DM algorithms for extracting regularities (e.g.,
patterns, association rules, clusters etc) from data. In
doing this, OLAM realizes a proper KDD process.
Figure 1: A reference architecture for OLAM.
OLAM was proposed by Han in his fundamental
paper (Han, 1997), along with the OLAP-based DM
system
DBMiner (Han et al., 1996), which can be
reasonably considered as the practical
implementation of OLAM. In order to emphasize
and refine the capability of discovering useful
knowledge from huge amounts of data, OLAM gets
the best of both technologies (i.e., OLAP and DM).
From OLAP, (i) the excellent capability of storing
data, which has been of relevant interest during the
last years (e.g., (Harinarayan et al., 1996)), (ii) the
support for multidimensional and multi-resolution
data analysis (Chaudhuri et al., 1997); (iii) the
richness of OLAP operators (Han & Kamber, 200),
such as roll-up, drill-down, slice-&-dice, pivot etc;
(iv) the wide availability of a number of query
classes, such as range-queries (Ho et al., 1997),
which have been extensively studied during the last
years, and can be used as baseline for implementing
even-complex KDD tasks. From DM, the broad
collection of techniques available in literature, each
of them oriented to cover a specific KDD task;
among these techniques, some are relevant for
OLAM, such as: mining association rules in
transactional or relational databases, mining
classification rules, cluster analysis, summarizing
and generalizing data using data cube or attribute-
oriented inductive approaches.
MRE-KDD+: A MULTI-RESOLUTION, ENSEMBLE-BASED MODEL FOR ADVANCED KNOLWEDGE
DISCOVERY
153

A reference architecture for OLAM is depicted
in Figure 1 (Han & Kamber, 2000). Here, the OLAP
Engine and the OLAM Engine run in a combined
manner in order to extract useful knowledge from a
collection of subject-oriented data marts. Beyond the
above-described OLAM features, this architecture
also supports a leading OLAM functionality, the so-
called On-Line Interactive Mining (Han & Kamber,
2000), which consists in iteratively executing DM
algorithms over different views extracted from the
same data mart. In this case, the effective “add-on”
value given by OLAP is represented by a powerful
information gain which cannot be easily supported
by traditional OLTP operators/tools, without
introducing excessive computational overheads.
While there are in literature a plethora of data
representation techniques and DM algorithms, each
of then developed for a particular application
scenario, frameworks that integrate with-a-large-
vision several techniques coming from different
contexts via synthesizing data warehousing, DM and
KDD principles are very few. Furthermore, while
there exist an extremely wide set of DM and KDD
tools (a comprehensive overview can be found in
(Goebel & Gruenwald, 1999)), mainly focused to
cover a specific KDD task (e.g., association rule
discovery, classification, clustering etc), very few of
them integrate heterogeneous KDD-oriented
techniques and methodologies in a unique
environment. Along these, the most significant
experiences that have deeply influenced our work
are
DBMiner and WEKA (Witten & Frank, 2005). In
the following, we refer to both the environments in
the vest of “realizations” of the respective
underlying models.
DBMiner is a powerful OLAM-inspired system
which allows us to (i) extract and represent
knowledge from large databases and data
warehouses, and (ii) mine knowledge via a wide set
of very useful data analysis functionalities, mainly
OLAP-inspired, such as data/patterns/results browse,
exploration, visualization and intelligent querying.
Specifically, at the representation/storage layer,
DBMiner makes use of the popular data cube model
(the foundation of OLAP), first proposed by Gray et
al. (1997), where relational data are aggregated on
the basis of a multidimensional and multi-resolution
vision of data. Based on the data cube model,
DBMiner makes available to the user a wide set of
innovative functionalities ranging from time-series
analysis to prediction of the data distribution of
relational attributes to mining of complex objects
(like those that one can find in a GIS); furthermore,
DBMiner also offers a data mining query language,
called DMQL, for supporting the standardization of
DM functionalities and their integration with
conventional DBMS. Finally, the graphical user
interface of
DBMiner supports various attracting,
user-friendly forms implementing the above-listed
features.
WEKA is a Machine Learning (ML) environment
for efficiently supporting DM activities against large
databases, and it has been designed to aid in decision
support processes in order to understand which
information is relevant for the specific context, and,
consequently, make prediction faster. Similarly to
DBMiner, WEKA offers a graphical environment
where users can (i) edit a ML technique, (ii) test it
against external data sets, and (iii) study its
performance under the stressing of various metrics.
Moreover,
WEKA users, just like DBMiner users, are
allowed to mine the output knowledge of ML
techniques by means of several advanced intelligent
visualization components. Contrarily to
DBMiner,
WEKA does not make use of a particular data-
representation/storage solution to improve data
access/management/processing.
Finally, due to the nature and the goals of both
the outlined environments/models, we can claim that
DBMiner is closer to our work rather than WEKA.
3 MRE-KDD+: PRINCIPLES
AND THEORETICAL
FOUNDATIONS
MRE-KDD
+
is the innovative model we propose,
and it has been designed to efficiently support
advanced knowledge discovery from large databases
and data warehouses according to a multi-resolution,
ensemble-based approach. Basically, MRE-
KDD
+
follows the approach (Han, 1997), which,
as highlighted in Section 2, is the state-of-the-art for
OLAM.
3.1 MRE-KDD
+
OLAP-based Data
Representation and Management
Layer
Let S = {S
0
, S
1
, …, S
K-1
} be a set of K distributed
and heterogeneous data sources, and D = {D
0
, D
1
,
…, D
P-1
} be a set of P data marts defined over data
sources in S. The first component of MRE-KDD
+
is the so-called Multidimensional Mapping Function
MMF, defined as a tuple MMF = 〈MMF
H
,MMF
F
〉,
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154

which takes as input a sub-set of M data sources in
S, denoted by S
M
= {S
m
, S
m+1
, …, S
m+M-1
}, and
returns as output a data mart D
k
in D, computed
over data sources in S
M
according to the construct
MMF
H
that models the definition of D
k
. MMF
H
is in
turn implemented as a conventional OLAP
conceptual schema, such as star- or snowflake-
schemas (Han & Kamber, 2000).
MMF
F
is the
construct of
MMF that properly models the
underlying function, defined as follows:
MMF
F
: S → D
(1)
Given a
MMF G, we introduce the concept of
degree of G, denoted by G
Δ
, which is defined as the
number of data sources in S over which the data
mart provided by G (i.e., D
k
) is computed, i.e. G
Δ
≡
|S
M
|.
Due to the strongly “data-centric” nature of
MRE-KDD
+
, management of OLAP data
assumes a critical role, also with respect to
performance issues, which must be taken in relevant
consideration in data-intensive applications like
those addressed by OLAM. To this end, we
introduce the Multidimensional Cubing Function
MCF, defined as a tuple MCF = 〈MCF
H
,MCF
F
〉,
which takes as input a data mart D
k
in D, and
returns as output a data mart D
h
in D, according to
the construct
MCF
H
that models an OLAP
operator/tool. In more detail,
MCF
H
can be one of
the following OLAP operators/tools:
 Multidimensional View Extraction V, which
computes D
h
as a multidimensional view
extracted from D
k
by means of a set of ranges
R
0
, R
1
, …, R
N-1
defined on the N dimensions of
D
k
d
0
, d
1
, …, d
N-1
, respectively, being each
range R
j
defined as a tuple R
j
= 〈L
l
,L
u
〉, with L
l
< L
u
, such that L
l
is the lower and L
u
is the
upper bound on d
j
, respectively;
 Range Aggregate Query Q, which computes
D
h
as a one-dimensional view (i.e., an
aggregate value) given by the application of a
SQL aggregate operator (such as SUM,
COUNT, AVG etc) applied to the collection
of (OLAP) cells contained within a
multidimensional view extracted from D
k
by
means of the operator V;
 Top-K Query K, which computes D
h
as a
multidimensional view extracted from D
k
by
means of the operator V, and containing the
(OLAP) cells of D
k
whose values are the first
K greatest values among cells in D
k
;
 Drill-Down U, which computes D
h
via
decreasing the level of detail of data in D
k
;
 Roll-Up R, which computes D
h
via increasing
the level of detail of data in D
k
;
 Pivot P, which computes D
h
via re-structuring
the dimensions of D
k
(e.g., changing the
ordering of the dimensions).
Formally,
MCF
H
= {V, Q, K, U, R, P}.
Finally,
MCF
F
is the construct of MCF that properly
models the underlying function, defined as follows:
MCF
F
: D → D
(2)
It should be noted that the construct
MCF
H
of
MCF operates on a singleton data mart to extract
another data mart. In order to improve the quality of
the overall KDD process, we also introduce the
Extended Multidimensional Cubing Function
MCF
E
,
defined as a tuple
MCF
E
= 〈MCF
E
H
,MCF
F
〉, which
extends
MCF by providing a different, complex
OLAP operator/tool (i.e.,
MCF
E
H
) instead that the
“basic”
MCF
H
. MCF
E
H
supports the amenity of
executing
MCF
H
over multiple data marts, modeled
as a sub-set of B data marts in D, denoted by D
B
=
{D
b
, D
b+1
, …, D
b+B-1
}, being these data marts
combined by means of the operator JOIN performed
with respect to schemas of data marts. Specifically,
MCF
E
H
operates according to two variants: (i) in the
first one, we first apply an instance of
MCF
H
to each
data mart in D
B
, thus obtaining a set of transformed
data marts D
T
, and then the operator JOIN to data
marts in D
T
; (ii) in the second one, we first apply
the operator JOIN to data marts in D
B
, thus
obtaining a unique data mart D
U
, and then an
instance of
MCF
H
to the data mart D
U
.
To give examples, let D
B
= {D
0
, D
1
, D
2
} be the
target sub-set of data marts, then, according to the
first variant, a possible instance of
MCF
E
H
could be:
V(D
0
) ZY K(D
1
) ZY U(D
2
); contrarily to this,
according to the second variant, a possible instance
of
MCF
E
H
could be: U(D
0
ZY D
1
ZY D
2
). Note
that, in both cases, the result of the operation is still
a data mart belonging to the set of data marts D of
MRE-KDD
+
.
MRE-KDD+: A MULTI-RESOLUTION, ENSEMBLE-BASED MODEL FOR ADVANCED KNOLWEDGE
DISCOVERY
155

Formally, we model
MCF
E
H
as a tuple MCF
E
H
=
〈D
B
,Y〉, such that (i) D
B
is the sub-set of data marts
in D on which
MCF
E
H
operates to extract the final
data mart, and (ii) Y is the set of instances of
MCF
H
used to accomplish this goal.
3.2 MRE-KDD
+
Data Mining Layer
DM algorithms defined in MRE-KDD
+
are
modeled by the set A = {A
0
, A
1
, …, A
T-1
}; these
are classical DM algorithms focused to cover
specific instances of consolidated KDD tasks, such
as discovery of patterns and regularities, discovery
of association rules, classification, clustering etc,
with the novelty of being applied to
multidimensional views (or, equally, data marts)
extracted from the data mart domain D of MRE-
KDD
+
via complex OLAP operators/tools
implemented by the components
MCF and MCF
E
.
Formally, an algorithm A
h
of A in MRE-KDD
+
is modeled as a tuple A
h
= 〈I
h
,D
h
,O
h
〉, such that: (i)
I
h
is the instance of A
h
(properly, A
h
models the
class of the particular DM algorithm), (ii) D
h
is the
data mart on which A
h
executes to extract
knowledge, and (iii) O
h
is the output knowledge of
A
h
. Specifically, O
h
representation depends on the
nature of algorithm A
h
, meaning that if, for
instance, A
h
is a clustering algorithm, then O
h
is
represented as a collection of clusters (reasonably,
modeled as sets of items) extracted from D
h
.
KDD process in MRE-KDD
+
are governed by
the component Execution Scheme, denoted by ES,
which rigorously models how algorithms in A must
be executed over multidimensional views of D. To
this end,
ES establishes (i) how to combine
multidimensional views and DM algorithms (i.e.,
which algorithm must be executed on which view),
and (ii) the temporal sequence of executions of DM
algorithms over multidimensional views. To formal
model this aspect of the framework, we introduce
the Knowledge Discovery Function
KDF, which
takes as input a collection of R algorithms A
R
=
{A
r
, A
r+1
, …, A
r+R-1
} and a collection of W data
marts D
W
= {D
w
, D
w+1
, …, D
w+W-1
}, and returns as
output an execution scheme ES
p
. KDF is defined as
follows:
KDF: A
R
× D
W
→ 〈I
R
× D
T
,ϕ〉
(3)
such that: (i) I
R
is a collection of instances of
algorithms in A
R
, (ii) D
T
is a collection of
transformed data marts obtained from D
W
by means
of cubing operations provided by the components
MCF or MCF
E
of the framework, and (iii) ϕ is a
collection determining the temporal sequence of
instances of algorithms in I
R
over data marts in D
T
in terms of ordered pairs 〈I
r
,D
T
k
〉, such that the
ordering of pairs indicates the temporal ordering of
executions. From (3), we derive the formal
definition of the component
ES of MRE-KDD
+
as follows:
ES = 〈I × D,ϕ〉
(4)
Finally, the execution scheme ES
p
provided by
KDF can be one of the following alternatives:
 Singleton Execution 〈I
r
× D
T
k
,ϕ〉: execution of
the instance I
r
of the algorithm A
r
over the
transformed data mart D
T
k
, with ϕ =
{〈I
r
,D
T
k
〉}.
 1 × N Multiple Execution 〈I
r
× {D
T
k
, D
T
k+1
, …,
D
T
k+N-1
},ϕ〉: execution of the instance I
r
of the
algorithm A
r
over the collection of
transformed data marts {D
T
k
, D
T
k+1
, …,
D
T
k+N-1
}, with ϕ = {〈I
r
,D
T
k
〉, 〈I
r
,D
T
k+1
〉, …,
〈I
r
,D
T
k+N-1
〉}.
 N × 1 Multiple Execution 〈{I
r
, I
r+1
, …, I
r+N-1
} ×
D
T
k
,ϕ〉: execution of the collection of
instances {I
r
, I
r+1
, …, I
r+N-1
} of the algorithms
{A
r
, A
r+1
, …, A
r+N-1
} over the transformed
data mart D
T
k
, with ϕ = {〈I
r
,D
T
k
〉, 〈I
r+1
,D
T
k
〉,
…, 〈I
r+N-1
,D
T
k
〉}.
 N × M Multiple Execution 〈{I
r
, I
r+1
, …, I
r+N-1
}
× {D
T
k
, D
T
k+1
, …, D
T
k+M-1
},ϕ〉: execution of
the collection of instances {I
r
, I
r+1
, …, I
r+N-1
}
of the algorithms {A
r
, A
r+1
, …, A
r+N-1
} over
the collection of transformed data marts {D
T
k
,
D
T
k+1
, …, D
T
k+M-1
}, with ϕ = {…,
〈I
r+p
,D
T
k+q
〉, …}, such that 0 ≤ p ≤ N – 1 and
0 ≤ q ≤ M – 1.
3.3 MRE-KDD
+
Ensemble Layer
As stated in Section 1, at the output layer, MRE-
KDD
+
adopts an ensemble-based approach. The
so-called Mining Results (MR) coming from the
executions of DM algorithms over collections of
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156

data marts must be finally merged in order to
provide the end-user/application with the extracted
knowledge. It should be noted that this is a relevant
task in our proposed framework, as very often end-
users/applications are interested in extracting useful
knowledge by means of correlated, cross-
comparative KDD tasks, rather than a singleton
KDD task, according to real-life DM scenarios.
Combining results coming from different DM
algorithms is a non-trivial research issue, as
recognized in literature. In fact, as highlighted in
Section 4.2, the output of a DM algorithm depends
on the nature of that algorithm, so that in some cases
MR coming from very different algorithms cannot
be combined directly.
In MRE-KDD
+
, we face-off this problematic
issue by making use of OLAP technology again. We
build multidimensional views over MR provided by
execution schemes of
KDF, thus giving support to a
unifying manner of exploring and analyzing final
results. It should be noted that this approach is well-
motivated under noticing that usually end-
user/applications are interested in analyzing final
results based on a certain mining metrics provided
by KDD processes (e.g., confidence interval of
association rules, density of clusters, recall of IR-
style tasks etc), and this way-to-do is perfectly
suitable to be implemented within OLAP data cubes
where (i) data source is the output of DM algorithms
(e.g., item sets), (ii) (OLAP) dimensions are user-
selected features of the output of DM algorithms,
and (iii) (OLAP) measures are the above-mentioned
mining metrics. Furthermore, this approach also
involves in the benefit of efficiently supporting the
visualization of final results by mean of attracting
user-friendly, graphical formats/tools such as
multidimensional bars, charts, plots etc, similarly to
the functionalities supported by
DBMiner and
WEKA.
Multidimensional Ensembling Function
MEF is
the component of MRE-KDD
+
which is in charge
of supporting the above-described knowledge
presentation/delivery task. It takes as input a
collection of Q output results O = {O
0
, O
1
, …, O
Q-1
}
provided by
KDF-formatted execution schemes and
the definition of a data mart Z, and returns as output
a data mart L, which we name as Knowledge
Visualization Data Mart (KVDM), built over data in
O according to Z. Formally,
MEF is defined as
follows:
MEF: 〈O,Z〉 → D
(5)
It is a matter to note that the KVDM L becomes
part of the set of data marts D of MRE-KDD
+
,
but, contrarily to the previous data marts, which are
used to knowledge processing purposes, it is used to
knowledge exploration/visualization purposes.
4 CONCLUSIONS AND FUTURE
WORK
Starting from successful OLAM technologies, in this
paper we have presented MRE-KDD
+
, a model
for supporting advanced knowledge discovery from
large databases and data warehouses, which is useful
for any data-intensive setting.
Future work is oriented along two main
directions: (i) testing the performance of MRE-
KDD
+
against real-life scenarios such as those
drawn by distributed corporate data warehousing
environments in B2B and B2C e-commerce systems,
and (ii) extending the actual capabilities of MRE-
KDD
+
as to embed novel functionalities for
supporting prediction of events in new DM activities
edited by users/applications on the basis of the
“history” given by logs of previous KDD processes
implemented in similar or correlated application
scenarios.
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