Towards Analytical MD Stars from Linked Data
Victoria Nebot and Rafael Berlanga
Computer Languages and Systems, Universitat Jaume I, Castell
´
on, Spain
Keywords:
Linked Data, RDF, Multidimensional Models, Statistical Models.
Abstract:
While the Linked Data (LD) initiative has given place to open, large amounts of semi-structured and rich data
published on the Web, effective analytical tools that go beyond browsing and querying are still lacking. To
address this issue, we propose the automatic generation of multidimensional (MD) analytical stars. The success
of the MD model for data analysis has been in great part due to its simplicity. Therefore, in this paper we aim
at automatically discovering MD conceptual patterns that summarize LD. These patterns resemble the MD star
schema typical of relational data warehousing. Our method is based on probabilistic graphical models and
makes use of the statistics about the instance data to generate the MD stars. We present a first implementation,
and the preliminary results with large LD sets are encouraging to further work in this direction.
1 INTRODUCTION
During the last years, communities from different ar-
eas have published data in the cloud of Linked Data
(LD) following the publication guidelines, providing
the basis for creating and populating the Web of Data.
Currently, there are approximately 13 billion triples
over 200 datasets.
The increasing availability of these semi-
structured and semantically enriched datasets has
prompted the need for new tools able to explore,
query, analyze and visualize these semi-structured
data (Dadzie and Rowe, 2011). While several
different tools such as graph-based query builders,
semantic browsers and exploration tools (Auer and
Lehmann, 2007; Berners-Lee et al., 2006; Heim et al.,
2010; Ara
´
ujo and Schwabe, 2009) have emerged to
aid the user in querying, browsing and exploring LD,
these approaches have a limited ability to summarize,
aggregate and display data in the form that a scientific
or business user expects, such as tables and graphs.
Moreover, they fall short when it comes to provide
the user an overview of the data that may be of
interest from an analytical viewpoint.
LD constitutes a valuable source of knowledge
worth exploiting using analytical tools. Business In-
telligence (BI) uses the multidimensional (MD) model
to view and analyze data in terms of dimensions and
measures, which seems the most natural way to ar-
range data. BI has traditionally been applied to inter-
nal, corporate and structured data, which is extracted,
transformed and loaded (ETL) into a pre-defined and
static MD model. The relational implementation of
the MD data model is typically a star schema. The
dynamic and semi-structured nature of LD poses sev-
eral challenges to both potential analysts and current
BI tools. On one hand, exploring the datasets using
the available browsers and tools to find MD patterns is
cumbersome due to the semi-structured nature of the
data and the lack of support for obtaining summaries
of the data. Moreover, as the datasets are dynamic
their structure may change or evolve, making the one-
time MD design approach unfeasible.
In this paper, we aim at discovering candidate MD
patterns hidden in LD by suggesting the user MD an-
alytical stars using a statistical approach. A MD an-
alytical star is a MD star-shaped pattern at the con-
cept level that encapsulates an interesting MD analy-
sis (Nebot and Berlanga, 2012). These stars reflect the
most relevant patterns in the dataset, as they are cal-
culated from the instance data. Moreover, we ensure
that each MD analytical star has a minimum aggrega-
tion power, that is, it is able to provide a summary
of the data that it represents. By suggesting the user
these MD stars from large LD sets we are freeing the
user from the cumbersome task of browsing and ex-
ploring the data to find interesting analytical patterns.
We summarize our contribution as follows:
• We define the concept of MD analytical star as a
mapping of the MD model to LD. That is, we iden-
tify the subject of analysis, dimensions and mea-
sures that compose a MD analytical star in LD.
117
Nebot V. and Berlanga R..
Towards Analytical MD Stars from Linked Data.
DOI: 10.5220/0005128701170125
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2014), pages 117-125
ISBN: 978-989-758-048-2
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

• We model the problem of automatically discover-
ing MD analytical stars by means of probabilistic
graphical models and use a statistical framework
based on instance data to implement it.
• We introduce the notion of aggregation power
(similar to the notion of functionality between
facts and dimensions in traditional data warehous-
ing) and make an estimation to filter MD analytical
stars according to this score.
• We present the first results of our method to ex-
tract MD analytical stars over two large and well-
known LD datasets.
The structure of the paper is as follows. In Section
2 we review the literature related to the problem of an-
alyzing LD. Section 3 presents the main foundations
that underlie our approach. In Section 4 we present a
model for MD analytical stars over LD sources. Sec-
tion 5 contains the implementation and in Sections 6
and 7 we present the first results and give some con-
clusions and future work.
2 RELATED WORK
We have performed a thorough review on the litera-
ture from an analytical viewpoint to find out that the
majority of approaches use querying, exploration and
only light-weight analytics over LD.
For querying LD, SPARQL has become the de-facto
standard. However, directly querying a dataset using
SPARQL interface cannot be considered an end user
task as it requires familiarity with its syntax and the
structure of the underlying data. Graph-based query
builders such as (Auer and Lehmann, 2007) can help
users build triple patterns by using auto-completion to
express queries. However, users do not always have
explicit queries upfront, but need to explore the avail-
able data first in order to find out what information
might be interesting to them. Sgvizler
1
allows to ren-
der results of SPARQL queries as charts, maps, etc.
However, it requires SPARQL knowledge and focuses
only on the visualization part.
The review in (Dadzie and Rowe, 2011) about vi-
sualization and exploration of LD concludes that most
of the tools are designed for technical users and do
not provide an overview or summary on the data.
LD browsers such as (Berners-Lee et al., 2006;
Ara
´
ujo and Schwabe, 2009; Zviedris and Barzdins,
2011) are designed to display one entity at a time and
do not support the user in aggregation tasks. Most of
them use faceted filtering to better guide the user in
1
http://dev.data2000.no/sgvizler/
exploration tasks. However, the user gets overview of
only a small part of the dataset. On the other hand,
browsers such as (Schraefel et al., 2004) and (Stadler
et al., 2012) provide a more powerful browsing envi-
ronment, but are tailored to a specific application.
Graph-based tools such as RDF-Gravity
2
, IsaViz
3
or Relfinder (Heim et al., 2010) provide node-link vi-
sualizations of the datasets and the relationships be-
tween them. Although this approach can help obtain
a better understanding of the data structure, in some
cases graph visualization does not scale well to large
datasets.
The CODE Query Wizard and Vis Wizard devel-
oped under the CODE project
4
are a web-based vi-
sual analytics platform that enables non-expert users
to easily perform exploration and lightweight analytic
tasks on LD. Still, the user has to browse the data
to find interesting analytical queries. Payola (Klimek
et al., 2013) is a framework that allows any expert
user to access a SPARQL endpoint, perform analysis
using SPARQL queries and visualize the results using
a library of visualizers.
We claim that existing tools for exploration and
analysis of LD provide little or no support for sum-
maries so that the user can have an idea of the struc-
ture of the dataset and the parts that seem more in-
teresting for analysis. In that line, we have also
looked into approaches that provide graph summaries
over LD using different techniques such as bisim-
ulation and clustering (Alzogbi and Lausen, 2013;
Khatchadourian and Consens, 2010). However, these
graph summaries are produced without an analytical
focus, therefore, the resulting summaries may not be
useful for analysis purposes.
Recently, there have been some attempts to an-
alyze LD that go beyond querying and browsing.
(Nebot and Berlanga, 2012) proposes MD analysis
over LD under the OWL formalism. Other approaches
(K
¨
ampgen and Harth, 2011; Etcheverry and Vaisman,
2012) have proposed MD analysis over LD relying on
the previous manual annotation of the MD elements
(dimensions and measures) and using previously de-
fined MD vocabularies.
3 FOUNDATIONS
In this section, we review the main foundations
that underlie our approach.
2
http://semweb.salzburgresearch.at/apps/rdf-gravity/
3
http://www.w3.org/2001/11/IsaViz/
4
http://code-research.eu/
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3.1 Linked Data
LD is a set of common practices and general rules
to contribute to the Web of Data (Heath and Bizer,
2011). The basic principles are that each entity should
be assigned a unique URL identifier, the identifiers
should be dereferenceable by HTTP and the entity
representations should be interlinked together to form
a global LD cloud.
The most adopted standard to implement the Web
of Data is RDF (Klyne and Carroll., 2004), which al-
lows us to make statements about entities. It assumes
data modeled as triples with three components: sub-
ject, predicate and object. We consider only valid RDF
triples using URIs (U ), blank nodes (B) and literals
(L). These triples can also be viewed as graphs, where
vertices correspond to subjects and objects, while la-
beled edges represent the triples themselves. SPARQL
(Prudhommeaux and Seaborne, 2008) has become the
standard for querying RDF data and it is based on the
specification of triple patterns.
In RDF there is no technical distinction between
the schema and the instance data, even though it
provides terminology to express class membership
(rdf:type). The RDFS extension allows to create tax-
onomies of classes and properties. It also extends def-
initions for some of the elements of RDF, for example
it sets the domain and range of properties and relates
the RDF classes and properties into taxonomies us-
ing the RDFS vocabulary. OWL extends RDFS and al-
lows for expressing further schema definitions in RDF.
The formal semantics of RDFS and OWL enrich RDF
with implicit information that can be reasoned over.
Throughout the paper, we refer both to the explicit
and implicit triples, which have been derived using
some reasoning mechanism. We use the naming con-
vention of OWL referring to classes, properties and
individuals to homogenize terminology.
3.2 Multidimensional Models
The MD model is the conceptual abstraction mostly
used in BI. The observations or facts are analyzed
in terms of dimensions and measures (Kimball and
Ross, 2011). They focus on a subject of analysis (e.g.,
sales) and define a series of dimensions or different
analysis perspectives (e.g., location, time, product),
which provide contextual information. Facts are ag-
gregated in terms of a series of measures (e.g., aver-
age sales). As a result, analysts are able to explore
and query the resulting data cube applying OLAP op-
erations. A typical query would be to display the evo-
lution of the sales during the current year of personal
care products by city.
BI has traditionally been applied to internal, cor-
porate and structured data, which is extracted, trans-
formed and loaded into a pre-defined and static MD
model. The relational implementation of the MD data
model is typically a star schema, where the fact table
containing the summarized data is in the center and is
connected to the different dimension tables by means
of a functional relation.
3.3 Bayesian Networks
A Bayesian network provides a graph theoretic repre-
sentation to compactly represent the joint probability
distribution of random variables in a problem domain.
Formally, a Bayesian network consists of two compo-
nents: structure and parameters. The structure is rep-
resented as a directed acyclic graph (DAG) G which
consists of a set of vertices V and a set of edges E
that connects these vertices, that is, G = (V,E). The
set of vertices corresponds to random variables in a
problem domain while the set of edges defines certain
types of conditional dependency among these vari-
ables. Parameters, on the other hand, describe condi-
tional probability distribution of each variable given
its parents in G. These conditional probabilities to-
gether with the Markov property assumption, that is ,
each variable x
i
is independent of its non-descendent
given its parents, simplifies the computation of joint
probability distribution of these variables.
P(x
1
,x
2
,...,x
n
) =
n
∏
i=1
P(x
i
|pa(x
i
)) (1)
where pa(x
i
) represents the set of parents of vari-
able x
i
.
4 MD ANALYTICAL STARS
In this section we explain how we model MD analyti-
cal stars from LD.
We formalize the representation of an RDF graph
using graph notation.
Definition 4.1. (RDF graph) An RDF graph G is a
labeled directed graph G = hV,E,λi where:
• V is the set of nodes, let V
0
denote the nodes in V
having no outgoing edge, and let V
>0
= V \V
0
;
• E ⊆ V ×V is the set of directed edges;
• λ : V ∪ E → U ∪ B ∪ L is a labeling function such
that λ
|V
is injective, with λ
|V
0
: V
0
→ U ∪ B ∪ L
and λ
|V
>0
: V
>0
→ U ∪ B, and λ
|E
: E → U.
Typical analysis usually involves investigating a
set of particular facts according to relevant criteria
TowardsAnalyticalMDStarsfromLinkedData
119

(dimensions) and measurable attributes (measures).
Here, we use the notion of basic graph pattern (BGP)
queries, which is a well-known a subset of SPARQL.
A BGP is a set of triple patterns, where each triple has
a subject, predicate and object, some of which can be
variables. We are specially interested in rooted BGP
queries, as they resemble the star-shaped pattern typ-
ical of MD analysis.
Definition 4.2. (Rooted query) Let q be a BGP query,
G = hV, E, λi its graph and v ∈ V a node that is a vari-
able in q. The query q is rooted in v iff G is a con-
nected graph and any other node v
0
∈ V is reachable
from v following the directed edges in E.
Example 4.1. (Rooted query) The query q is a rooted
BGP query, with x
1
as root node.
q(x
1
,x
2
,x
3
,x
5
) :- x
1
carbonemissions23kg x
3
,
x
1
state x
2
,
x
1
fuel type x
4
, x
4
label x
5
The query’s graph representation below shows
that every node is reachable from the root x
1
.
Even though rooted queries express data patterns
by means of the predicate chains, these are still vague
as the variable nodes can match any element in U ∪
B ∪ L. To narrow down the scope of the patterns we
define the notion of typified rooted queries as follows:
Definition 4.3. (Typified rooted query) A typified
rooted query q
0
is a rooted query with graph G =
hV,E,λi where each variable node v
x
∈ V has an as-
sociated class or datatype. That is, each variable v
x
has an outgoing edge (v
x
,v
y
) such that λ((v
x
,v
y
)) =
rdf:type and λ(v
y
) ∈ U and v
y
has an outgoing edge
(v
y
,v
z
) such that λ((v
y
,v
z
)) = rdf:type and λ(v
z
) ∈
{rdfs:Class, rdfs:Datatype}.
Example 4.2. (Typified rooted query) The previous
query q can be typified as follows:
q(x
1
,x
2
,x
3
,x
5
) :- x
1
rdf:type Powerplant,
Powerplant rdf:type rdfs:Class, x
1
state x
2
,
x
2
rdf:type Country, Country rdf:type rdfs:Class,
x
1
carbonemissions23kg x
3
, x
3
rdf:type xsd:float,
xsd:float rdf:type rdfs:Datatype,x
1
fuel type x
4
,
x
4
rdf:type Fuel, Fuel rdf:type rdfs:Class,
x
4
label x
5
, x
5
rdf:type xsd:string,
xsd:string rdf:type rdfs:Datatype
From now on, we omit the type edges and repre-
sent typified rooted queries with the (data)type’s name
in the variable node.
It is immediate to see that a typified rooted query
is composed by a set of typified paths that go from
the root to a sink node (node with no outgoing edges).
The root node represents a class and the sink node
represents either a class or a datatype. We formalize
this notion next:
Definition 4.4. (Typified path) Given a typified
rooted query q with x
1
as root node and graph G =
hV,E,λi, a typified path is a sequence p = c
1
− r
1
−
c
2
− r
2
− ... − r
n−1
− c
f
where λ(x
1
) = c
1
is the root
class, c
f
is a sink class or datatype, every r
i
is a prop-
erty and every c
i
has an associated class.
Example 4.3. (Typified path) In the previous query
q we can identify the following typified paths:
(Powerplant, state, Country)
(Powerplant, carbonemissions-23kg, float)
(Powerplant, fuel type, Fuel, label, string)
In MD modeling it is important the many-to-one
relation between facts and dimensions to ensure ag-
gregation power. That is, one fact must be associ-
ated with one dimension value, whereas a dimension
value can and should be associated to multiple facts.
In our LD scenario, we define the aggregation power
of a typified path as follows:
Definition 4.5. (Aggregation power) Given a typi-
fied path p = c
1
− r
1
− c
2
− r
2
− ... − r
n−1
− c
f
, the
aggregation power is calculated as the ratio between
the number of individuals of the root class c
1
and the
number of different individuals (or literals) of the sink
class (or datatype) c
f
that satisfy the path.
Example 4.4. (Aggregation power) Given the
number of individuals (or literals) in parenthesis that
satisfy the underlying queries of the paths, we show
their aggregation power:
(Powerplant
(160)
, state, Country
(13)
) → 12.3
(Powerplant
(11994)
, fuel type, Fuel,
label, string
(27)
→ 444.2
Notice that, in order to exactly calculate the aggre-
gation power, one must execute the query correspond-
ing to the typified path, which can imply several joins.
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As this is expensive and impractical, we have devised
a rough estimation of the aggregation power that will
be shown in the next section.
We are now ready to introduce MD analytical stars.
For this, we make use of traditional data warehousing
terminology. We use the notion of classifier to denote
the level of data aggregation, that is, the classifier de-
fines the dimensions according to which the facts will
be analyzed. The measure allows obtaining values to
be aggregated using aggregation functions.
Definition 4.6. (MD analytical star) Given an RDF
graph G = hV,E,λi, a MD analytical star rooted in the
node x ∈ V is a triple: S = hc(x, d
1
,...,d
n
),m(x,v),
L
i
where:
• c(x,d
1
,...,d
n
) is a typified query rooted in the
node r
c
of its graph G
c
, with λ(r
c
) = x and each
path x − ... −d
i
is a typified path. This is the clas-
sifier of x w.r.t. the n dimensions d
1
,...,d
n
. The
node x is the subject of analysis.
• m(x,v) is a typified query rooted in the node r
m
of
its graph G
m
, with λ(r
m
) = x. This query is only
composed by a typified path x − ... − v
5
. This is
called the measure of x.
•
L
is an aggregation function over a set of values,
that is, the aggregator for the measure of x w.r.t.
its classifier.
• Each of the typified paths of the classifier has an
aggregation power over a threshold δ.
Notice that typified rooted queries (and therefore,
typified paths) are the building block to suggest MD
analytical stars.
Example 4.5. (MD analytical star) The MD analytical
star below asks for the average of carbon emission of
powerplants, classified by country and fuel type.
hc(x,x
1
,x
3
),m(x,x
4
),averagei
where the classifier and measure queries are:
c(x,x
1
,x
3
) : − x rdf:type Powerplant,
x state x
1
, x
1
rdf:type Country,
x fuel type x
2
, x
2
rdf:type Fuel,
x
2
label x
3
, x
3
rdf:type xsd:string
m(x,x
4
) : − x rdf:type Powerplant ,
x carbonemissions-23kg x
4
,
x
4
rdf:type xsd:float
The answer to an MD analytical star is a set of tu-
ples of dimension values found in the answer of the
classifier query, together with the aggregated result of
the measure query. Therefore, it can be represented as
5
For the sake of simplicity, we assume that an MD ana-
lytical star has only one measure.
a cube of n dimensions, where each cell contains the
aggregated measure. However, query processing and
answering is out of the scope of this paper.
5 IMPLEMENTATION
In order to discover MD analytical stars we have to
find both the classifier and measure typified queries
rooted in a potential class acting as subject of analy-
sis. These typified queries are composed by typified
paths (from now on we call them simply paths) with
a certain aggregation power. In this section we sum-
marize all the steps followed to obtain MD analytical
stars.
5.1 Generation of Typified Triples
The paths that will form the MD analytical stars are
composed by typified triples. These are generated in
a pre-processing step as follows:
Given a LD set D, ∀c
1
,c
2
∈ D such that D |=
c
1
(x),c
2
(y),(x,r
1
,y), the triple (c
1
,r
1
,c
2
) is gener-
ated. We assume the existence of a reasoning system
able to infer the classes c
1
and c
2
of individuals x and
y.
5.2 Joint Probabilities of Typified Paths
We now focus on the automatic discovery of paths
from instance data starting from any potential subject
of analysis. We model the problem of finding paths
using probabilistic graphical models. In particular, we
model the probability of finding a path of length one
(c
1
,r
1
,c
2
), where c
1
,c
2
are classes and r
1
is a prop-
erty, as a Bayesian network where the random vari-
ables are the subject class c
1
, the property r
1
and the
object class c
2
. We observe that the property depends
on the subject, and the object depends on both the sub-
ject and the property.
To get the probability of observing a path,
p(c
1
,r
1
,c
2
), we factorize this probability using bi-
grams.
p(c
1
,r
1
,c
2
) =p(r
1
|c
1
) ∗ p(c
2
|r
1
,c
1
) =
p(r
1
|c
1
) ∗ p(c
2
|r
1
) ∗ p(c
2
,c
1
)
(2)
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121

To extend it to paths of arbitrary length, we simply
multiply the probabilities of the subsequent paths of
length one.
p(c
1
,r
1
,c
2
,r
2
,...,c
n
) =p(c
1
,r
1
,c
2
)∗
p(c
2
,r
2
,c
3
) ∗ ...∗
p(c
n−1
,r
n−1
,c
n
)
(3)
The joint probability of each class and property is
calculated from the collection of typified triples gen-
erated in the previous step. We estimate bi-gram prob-
abilities in the collection of typified triples through
MLE as follows:
p(w
2
|w
1
) =
count(w
1
,w
2
)
count(w
1
)
(4)
to estimate the probabilities p(r
1
|c
1
), p(c
2
|r
1
) and
p(c
2
,c
1
) for each typified triple (c
1
,r
1
,c
2
).
5.3 Typified Paths Generation
In this step we automatically build paths that will po-
tentially compose MD analytical stars. We explore the
underlying schema graph based on the previous es-
timated joint probabilities using a depth-first search
approach, shown in Algorithm 1. Starting from each
class (line 3 of GetPaths), the algorithm creates a one
node length path, path, composed by the source class
only and initializes the list probs to keep the joint
probability of each element in path. At each success-
ful recursion step in procedure GetPathsRec, the al-
gorithm extends the current explored path, p, with a
property r and a class or datatype node o based on
the joint probabilities p(r|c) (line 5), p(o|r) (line 8)
and p(o,c) (line 10). If these probabilities are over
some thresholds, the path is extended (line 14) and
added to the set of paths with an associated score (line
16). This score is the result of the product of the joint
probabilities of each element in the path. Finally, if
the latter added node is a class, the path is recursively
extended (line 19). In order to prune the search, we
have devised several thresholds. T HR
prob
filters out
joint probabilities that are too low to be considered
statistically significant. T HR
sc
filters out paths whose
final score is too low to be considered relevant. The
relative threshold avg
prob
(line 1) calculates at each
recursion step the average of the joint probabilities of
each element in the current path. It is used to not ex-
tend paths with elements whose joint probability is
lower than this threshold. This way, we avoid a possi-
ble incompleteness in the results when the probability
is lower than the average.
Algorithm 1: Typified paths discovery.
Procedure GETPATHS(D)
Input: D:dataset
Output: paths: tuples (path, score)
1: global paths = {}
2: global D
3: for c ∈ D, c is concept do
4: path = c
5: probs = []
6: GETPATHSREC(c,path,probs)
7: return paths
Procedure GETPATHSREC(c,p,probs)
Input: c: concept, p: current path, probs: path probs
1: avg
prob
= getAvg(probs)
2: if c in p then  cycle
3: paths = paths ∪ (p,sc)
4: for r ∈ D, r is role do
5: p
rc
= p(r|c)
6: if p
rc
< T HR
prob
∨ p
rc
< avg
prob
then return
7: for o ∈ D, o is concept do
8: p
or
= p(o|r)
9: if p
or
< T HR
prob
∨ p
or
< avg
prob
then return
10: p
oc
= p(o|c)
11: if p
oc
< T HR
prob
∨ p
oc
< avg
prob
then return
12: new
sc
= getScore(probs + [p
rc
, p
or
, p
oc
])
13: if new
sc
< T HR
sc
then return
14: new
p
= p + [r, o]
15: if (new
p
,new
sc
) /∈ paths then
16: paths = paths ∪ (new
p
,new
sc
)
17: if o is concept then
18: new
probs
= probs + [p
rc
, p
or
, p
oc
]
19: GETPATHSREC(o, new
p
, new
probs
)
5.4 Typified Paths Filtering by
Aggregation Power
Once we have obtained a set of paths from a source
class, we filter out those which do not pass the ag-
gregation power threshold δ, which has been set up
to 4. As previously said, calculating the aggregation
power of a path implies solving a query with poten-
tially several joins, and it results impractical to precal-
culate all possible paths with their associated aggrega-
tion power score. Thus, in an off-line pre-processing
step, we build an index I where we keep the num-
ber of individuals associated to each typified triple
t
i
= (c
1i
,r
i
,c
2i
). That is, for each such triple, we
calculate the number of individuals x of c
1i
and the
number of distinct individuals or literals y of c
2i
that
satisfy the triple (i.e., I[t
i
][c
1i
] = x and I[t
i
][c
2i
] = y).
Notice that for the object we keep the number of dis-
tinct individuals, as we are interested in discovering
groups.
Then, given a path p = t
1
t
2
...t
n
(composed by typ-
ified triples), we make a rough estimation of its aggre-
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122

gation power by calculating the ratio
a
b
, where a is the
number of individuals of the root class (i.e., I[t
1
][c
11
]),
and b has been calculated by carrying the minimum
score at each triple join. That is:
MIN
1≤i≤n
(I[t
i
][c
2i
],I[t
i+1
][c
1(i+1)
])
For example, having the following statistics about
typified triples:
I[(Powerplant, f uel type,Fuel)][Powerplant] = 12315
I[(Powerplant, f uel type,Fuel)][Fuel] = 30
I[(Fuel,label,string)][Fuel] = 27
I[(Fuel,label,string)][string] = 27
...
for the path (Powerplant, fuel type, Fuel, label,
xsd:string), we have that a = 12315 and b = 27, The
final aggregation power is
12315
27
= 456.1. Notice that
this estimation is optimistic, as we are assuming that
all the elements of one side of the join will join with
the other elements’ side.
5.5 Composing MD Analytical Stars
Finally, from the remaining paths, we select those
that will compose the classifier (i.e., dimensions) and
a set of possible measures. For this we use the
aggregation power of the path and the type of the
sink node. Paths ending in numeric datatypes (i.e.,
xsd:integer, xsd:float, xsd:double, etc.) and
with low aggregation power are considered measures,
whereas the rest of paths (i.e., paths ending in classes
or datatypes with high aggregation power) are con-
sidered dimensions and thus, are part of the classifier
query.
Currently, the generated MD analytical stars are
ranked based on an eigenvector centrality algorithm.
That is, stars whose subject of analysis is ranked
higher are displayed first (Zhang et al., 2007).
Computational complexity
Here we present a discussion about the computational
complexity of the whole process of generating MD
analytical stars. All the triples must be scanned in
order to generate their typified triples and calculate
their joint probabilities. The generation of typified
triples depends on the reasoning method used. If all
the triples are materialized, the process is O(N ×C
2
),
with N the number of triples and C the number of
classes, as the inference of the classes for each in-
stance is O(1) but each triple could generate up to
C
2
typified triples (C parents for the subject times C
parents for the object). However, this is highly un-
likely in practice. Otherwise, we must also consider
the reasoning time for each triple. The generation of
the joint probabilities for the typified triples is linear
with the number of typified triples. The generation of
typified paths (Algorithm 1) is O(C × (R +C)), with
C being the number of classes and R be the number
of properties. Such algorithm is an implementation
of DFS (i.e., it has complexity O(R +C)) and it is in-
voked once for each class. Notice that our implemen-
tation does not compute all the possible paths between
two classes, but only those which pass the thresholds,
thus the complexity for the DFS is much lower than
O(R +C). The filtering of the paths according to their
aggregation power is O(n×P), with P being the num-
ber of paths and n the maximum length of a path, as
the estimation of the aggregation power for each path
depends on its length. Finally, the composition of MD
analytical stars is O(P).
6 PRELIMINARY RESULTS
In this section we present the first results of our
method to build MD analytical stars from LD. We have
selected three LD datasets with different features to
test our method. BioPAX
6
is an emerging format for
sharing biological pathway data. We select the homo
sapiens pathways, which are available in RDF format.
Enipedia
7
is an initiative aimed at providing a collab-
orative environment through the use of wikis and the
Semantic Web for energy and industry issues. They
provide energy data from different open data sources
structured and linked in RDF. Dbpedia 3.9
8
is a com-
munity effort to extract structured information from
Wikipedia. They also make the information available
in RDF. Each dataset has different size and structure.
Biopax is the smallest one but is richer in terms of
semantics, whereas Enipedia and Dbpedia are much
larger but less semantically rich. Table 1 shows some
statistics about the datasets. We show both the num-
ber of triples, and the number of typified triples (see
Section 5.1), which demonstrates the big scale of the
scenario.
Table 1: Datasets statistics.
# triples # typified triples
Biopax 600,874 499,152
Enipedia 4,463,909 8,721,813
Dbpedia 25,896,867 253,599,827
To generate typified paths, we have empirically set
up T HR
prob
and T HR
sc
to 10
−2
and 10
−5
, respec-
tively. The aggregation power threshold δ is set up to
6
http://www.biopax.org/
7
http://enipedia.tudelft.nl/wiki/Main Page
8
http://wiki.dbpedia.org/Downloads39
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123

Table 3: MD analytical stars (Biopax).
Subject Paths (dimensions and measures)
Pathway name, xsd:string
(1,113) organism, bioSource
pathway-components, pathwayStep, step-interactions, pathway
xref, unificationXref, db, xsd:string
Catalysis direction, xsd:string
(2,125) control-type, xsd:string
controller, physicalEntityParticipant, cellular-location, openControlledVocabulary
controlled, biochemicalReaction
BiochemicalReaction name, string
(4,162 right, physicalEntityParticipant
left, physicalEntityParticipant
Table 2: Statistics about paths and MD stars.
# typ. paths # filt. paths # stars
Biopax 329 129 (39%) 20
Enipedia 643 369 (57%) 54
Dbpedia 12395 5809 (47%) 377
4. Table 2 shows the number of typified paths, paths
after filtering by aggregation power and the number
of analytical MD stars generated for each dataset.
We emphasize the usefulness of calculating typ-
ified paths as a means to capture and group together
instance data paths under the same semantic concepts,
providing a summarized overview of the structure of
the datasets. Yet, the amount of typified paths is too
large to be managed by an analyst. The aggregation
power property filters out about half of the typified
paths for Enipedia and Dbpedia datasets and even
more for Biopax. Finally, we observe that the num-
ber of MD analytical stars generated for each dataset
is manageable, compared to the dataset’s size, and
provides the analyst different interesting MD analy-
sis patterns. In Tables 3, 4 and 5 we show some ex-
cerpts of MD analytical stars for the three datasets.
Notice that not all the paths conforming the MD stars
are shown for space reasons. Paths in italics corre-
Table 4: MD analytical stars (Enipedia).
Subject Paths (dimensions and measures)
Powerplant Energyoutputnextdecade-23J, xsd:double
(34,632) Energyoutput-23J, xsd:double
Carbonemissions-23kg, xsd:double
country, Country
ownercompany, Company
Country NaturalGasProvenResources-23m3, xsd:double
(130) NaturalGasProduction-23m3, xsd:double
NaturalGasConsumption-23m3, xsd:double
label, xsd:string
NaturalGas- NumberOfTanks, xsd:double
Interconnector StorageCapacityLNG-23m3, xsd:double
(106) label, xsd:string
GasFlowsFrom, Country
GasFlowsTo, Country
spond to potential measures, whereas the rest act as
dimensions. The number in between parenthesis is
an estimation of the number of facts that satisfy the
shown star.
Table 5: MD analytical stars (Dbpedia).
Subject Paths (dimensions and measures)
Person birthPlace, Place
(795,564) deathPlace, Place
team, SportsTeam
birthDate, date
MusicGroup hometown, Place
(52,882) genre, Genre
recordLabel, Company
Educational- numberOfStudents, xsd:integer
Institution city, Place
(19,741) country, Country
foundingYear, xsd:gYear
Work runtime, xsd:double
(167,880) starring, Person
producer, Person
writer, Person
director, Person
genre, Genre
City elevation, xsd:double
(36,268) areaTotal, xsd:double
areaLand, xsd:double
areaWater, xsd:double
populationDensity, xsd:double
isPartOf, Place, country, Country
Film starring, Person
(65,826) writer, Person
musicComposer, Person
director, Person
director, Person, birthplace, Place
Automobile wheelbase, xsd:double
(4,333) length, xsd:double
transmission, xsd:string
assembly, Place
productionStartYear, xsd:gYear
productionEndYear, xsd:gYear
manufacturer, Company
engine, AutomobileEngine
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124

7 CONCLUSIONS AND FUTURE
WORK
In this paper, we have presented the first automatic
approach towards providing useful MD analytical pat-
terns from LD sources. The MD patterns are based
on the semantics of the data (i.e., they provide a con-
ceptual summary of the data), follow the MD model
(i.e., information is modeled in terms of analysis di-
mensions and measures) and are extracted following a
statistical approach. As this is preliminary work, there
is much room for improvement. In a near future, we
would like to explore more sophisticated and founda-
tional relative thresholds that help prunning the gen-
eration of paths. Also, we would like to devise a rank-
ing algorithm for the MD stars that takes into account
both the semantic and analytical relevance of the star.
Finally, as some of the stars are composed by many
semantically similar paths, it would be interesting to
further group these paths into semantic dimensions to
get an even more summarized view of the generated
stars.
REFERENCES
Alzogbi, A. and Lausen, G. (2013). Similar structures in-
side rdf-graphs. In LDOW, volume 996 of CEUR
Workshop Proceedings.
Ara
´
ujo, S. and Schwabe, D. (2009). Explorator: A tool
for exploring rdf data through direct manipulation. In
LDOW, volume 538 of CEUR Workshop Proceedings.
Auer, S. and Lehmann, J. (2007). What have innsbruck
and leipzig in common? extracting semantics from
wiki content. In Proc. of the 4th European Confer-
ence on The Semantic Web: Research and Applica-
tions, ESWC ’07, pages 503–517, Berlin, Heidelberg.
Berners-Lee, T., Chen, Y., Chilton, L., Connolly, D., Dha-
naraj, R., Hollenbach, J., Lerer, A., and Sheets, D.
(2006). Tabulator: Exploring and analyzing linked
data on the semantic web. In Proceedings of the 3rd
International Semantic Web User Interaction.
Dadzie, A. and Rowe, M. (2011). Approaches to visualising
linked data: A survey. Semant. web, 2(2):89–124.
Etcheverry, L. and Vaisman, A. A. (2012). Enhancing olap
analysis with web cubes. In ESWC, volume 7295 of
Lecture Notes in Computer Science, pages 469–483.
Heath, T. and Bizer, C. (2011). Linked Data: Evolving the
Web into a Global Data Space. Synthesis Lectures on
the Semantic Web. Morgan & Claypool Publishers.
Heim, P., Lohmann, S., and Stegemann, T. (2010). Inter-
active relationship discovery via the semantic web. In
Proc. of the 7th International Conference on The Se-
mantic Web: Research and Applications - Volume Part
I, ESWC’10, pages 303–317, Berlin, Heidelberg.
K
¨
ampgen, B. and Harth, A. (2011). Transforming sta-
tistical linked data for use in OLAP systems. In
I-SEMANTICS 2011, Graz, Austria, September 7-9,
2011, ACM Int. Conf. Proc. Series, pages 33–40.
Khatchadourian, S. and Consens, M. P. (2010). Explod:
Summary-based exploration of interlinking and rdf
usage in the linked open data cloud. In ESWC (2),
volume 6089 of Lecture Notes in Computer Science,
pages 272–287. Springer.
Kimball, R. and Ross, M. (2011). The Data Warehouse
Toolkit: The Complete Guide to Dimensional Model-
ing. Wiley.
Klimek, J., Helmich, J., and Neask, M. (2013). Payola:
Collaborative linked data analysis and visualization
framework. In The Semantic Web: ESWC 2013 Satel-
lite Events, volume 7955 of Lecture Notes in Com-
puter Science, pages 147–151.
Klyne, G. and Carroll., J. J. (2004). Resource description
framework (RDF): Concepts and abstract syntax.
Nebot, V. and Berlanga, R. (2012). Building data ware-
houses with semantic web data. Decision Support Sys-
tems, 52(4):853–868.
Prudhommeaux, E. and Seaborne, A. (2008). SPARQL
query language for RDF.
Schraefel, m. c., Shadbolt, N. R., Gibbins, N., Harris, S.,
and Glaser, H. (2004). CS AKTive Space: Represent-
ing computer science in the semantic web. In WWW,
pages 384–392, New York, NY, USA. ACM.
Stadler, C., Lehmann, J., H
¨
offner, K., and Auer, S. (2012).
Linkedgeodata: A core for a web of spatial open data.
Semantic Web Journal, 3(4):333–354.
Zhang, X., Cheng, G., and Qu, Y. (2007). Ontology summa-
rization based on rdf sentence graph. In WWW, pages
707–716. ACM.
Zviedris, M. and Barzdins, G. (2011). Viziquer: A tool
to explore and query sparql endpoints. In The Se-
manic Web: Research and App., volume 6644 of Lec-
ture Notes in Computer Science, pages 441–445.
TowardsAnalyticalMDStarsfromLinkedData
125