Domain Ontology for Time Series Provenance
Lucélia de Souza
1,2
, Maria Salete Marcon Gomes Vaz
2,3
and Marcos Sfair Sunye
2
1
Computer Science Department, State University of Center-West, Guarapuava, Paraná, Brazil
2
Informatics Department, Federal University of Paraná, Curitiba, Paraná, Brazil
3
Informatics Department, State University of Ponta Grossa, Ponta Grossa, Paraná, Brazil
Keywords: OWL, Modules, Time Series Processing, Trend Extraction, Nonstationary Time Series.
Abstract: Time series data are generated all the time with a volume without precedent, constituting themselves of a
points sequence spread out over time, usually at time regular intervals. Time series analysis is different from
data analysis, given its intrinsic nature, where observations are dependent and the observations order is
important for analysis. The knowledge about the data which will be analyzed is relevant in an analysis
process, but this knowledge is not always explicit and easy to interpret in many information resources. Time
series can be semantically enriched where provenance information using ontologies allows to representing
and inferring knowledge. The main contribution of this paper is to present a domain ontology developed by
modular design for time series provenance, which adds semantic knowledge and contributes to the choice of
appropriate statistical methods for an important step of time series analysis that is the trend extraction
(detrending). Trend is a time series component that needs be extracted because it can hide other phenomena,
as well as the most statistical methods are developed for stationary time series. With this work, is intended
to contribute for semantically improving the decision making about trend extraction step, facilitating the
preprocessing phase of time series analysis.
1 INTRODUCTION
The scientific knowledge generation, in several
domains, is related with the time series analysis,
from which is extracted useful information. Time
series data are characterized by way as they were
generated and collected, usually at time regular
intervals (Chandler and Scott, 2011; Cryer and
Chan, 2008).
Time series analysis is usually done in two
phases, preprocessing and data analysis, both
containing processing steps in order to obtain
scientific knowledge. Time series analysis is
different from data analysis, given its intrinsic
nature, where observations are dependent or
correlated and the observations order is important
for analysis. Statistical procedures and traditional
techniques based on assumptions of independent and
identically distributed data are not applied in time
series. This way, are necessary different methods of
analysis (Cryer and Chan, 2008).
In time series analysis, provenance information,
such as What the observation type of time series?,
How the time series were generated?, What is the
decomposition model used?, What assumptions were
considered?, How the time series data can be
classified according to assumptions?, What the trend
type considered?, among other information,
allowing the researcher to interpret the data better
and to use appropriate statistical methods,
specifically developed regarding its characteristics.
Hair et al (2010) asserts that the knowledge
about data that will be analyzed is important in an
analysis process. However, according to Hebeler et
al (2009), this is not present in several information
resources. Such knowledge is not always explicit
and easy to interpret. As well as in data analysis,
time series also can be semantically enriched where
provenance information using ontologies allows
representing and inferring knowledge.
This paper describes Time Series Ontology
(namespace tso:), a domain ontology (a module in
Ontology Web Language - OWL) with the definition
of main concepts and relationships involving time
series provenance. The proposed ontology adds
semantic knowledge in time series, contributing to
choose of appropriate statistical methods for an
important step of analysis that is the trend extraction,
also called detrending (Wu et al, 2007; Meinl, 2011).
Besides of this section, Section 2 describes time
217
de Souza L., Marcon Gomes Vaz M. and Sfair Sunye M..
Domain Ontology for Time Series Provenance.
DOI: 10.5220/0004886502170224
In Proceedings of the 16th International Conference on Enterprise Information Systems (ICEIS-2014), pages 217-224
ISBN: 978-989-758-028-4
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
series. The Section 3 relates ontologies and the
Section 4 reports time series provenance. Section 5
presents the development of the domain ontology.
Section 6 brings a comparison with related work.
Finally, Section 7 describes the conclusions and
future works perspectives.
2 TIME SERIES
Time series are an ordered sequence of observations,
usually obtained at time regular intervals (Chandler
and Scott, 2011; Cryer and Chan, 2008). Time series
are correlated data, being preferable the use of
analysis methods specifically developed to this data
type. Chandler and Scott (2011) explain that the
choice of appropriated methods of analysis depends
on questions of interest, where the knowledge about
time series data is essential.
The first step in any time series analysis is the
careful observation of plotted data over the time.
This procedure frequently suggests statistical
methods of analysis, as well as the statistics that
summarize the information about the data.
A time series can have the following classical
components (Meinl, 2011): Seasonal, Cyclic,
Irregular and Trend. In environmental sciences, the
trend is defined by Chandler and Scott (2011) as a
long-term temporal variation in statistics properties
of a process. However, the period of trend is
dependent of each application.
In environmental applications, among the
possible reasons for trend analysis stands out the
analysis of systems, where long-term changes can to
obscure aspects of real interest (Chandler and Scott,
2011). In this case, the first step in the time series
analysis is the identification and extraction of trend
to clearly understand the inter-relationships of data.
This paper is related with this reason, where trend is
clearly defined and needs to be extracted, otherwise
to make difficult the knowledge discovery process.
To many analyses, trend extraction is an
important step because it can to hide other
phenomena, as well as the most statistical methods
are developed for stationary time series (Montesino-
Pouzols and Lendasse, 2010). It making a stationary
time series means to extract all the deterministic
features, such as statistics measures of mean and
variance, in such way that correlations turn
themselves independent over time.
The need of modeling these and others
characteristics must be considered in order to
determine an adequate strategy in the analysis
(Chandler and Scott, 2011). The definitions and the
main features of the time series presented contribute
for the choice of appropriate statistical methods.
Such descriptions are considered in development of
the domain ontology as way of adding semantic
knowledge. The next section describes Ontologies
used to generation of time series provenance.
3 ONTOLOGIES
Ontology is a formal and explicit specification of a
shared conceptualization (Borst 1997). Kiryakov
(2006) defines ontology as a set of classes
representing concepts in domain, relationships
between concepts, axioms used to modeling
restrictions and rules and instances of classes,
constituting a knowledge base.
Guarino (1998) classifies ontologies according to
the generality level, where domain ontologies
constitute vocabularies about a generic domain. In
this work the domain of ontology is related with
time series provenance.
Although Resource Description Framework -
RDF and OWL were not developed to given support
for numeric concepts, because they depend on
schema definition and are based on the eXtensible
Markup Language - XML, the set of upper level
ontologies Semantic Web for Earth and
Environmental Terminology - SWEET
<http://sweet.jpl.nasa.gov/ontology/> is a good
example to integrate mathematical knowledge with
scientific application domains (Lange, 2013). In this
work some statements from SWEET are reused and
extended.
In the Semantic Web defined by Berners-Lee
(2001), the W3C Standard defines the effort of the
Linking Open Data (LOD) community where is
increased the number of data providers that
publishing and interlinking data on the web.
The actual web of data consists of billion of RDF
triples, in several domains. The DBpedia knowledge
base <http://wiki.dbpedia.org/About> is a central
hub of interlinking of the emerging data web, which
extracts structured information from Wikipedia and
makes them available on the web. In this work, some
instances of the classes of knowledge base are
associated with definitions from DBpedia, allowing
semantic interoperability.
The modularization involves identifying one or
more modules in ontology. A module is considered
as one significant and self-contained part of
ontology. Although there is no universal way for
modularization, the choosing of a particular
technique must be guided by application
ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems
218
requirements (Suárez-Figueroa et al, 2012). The next
section describes four use cases related with time
series provenance.
4 TIME SERIES PROVENANCE
There are many definitions for provenance in
literature (Moreau, 2010). Usually, it refers to origin
or source of something. The knowledge about the
data source in domains where the volume of data
that need to be analyzed is excessive, it contributes
to prove the correctness of resultant data, enabling
the understanding about how the data were
generated. Tan (2007) comments that provenance
information is considered as important as the result
itself.
Besides of ways coarse-grain and fine-grain to
generate provenance (Tan, 2007), another approach
to provenance considers the use of semantic
information based on ontologies, modeling concepts
and relationships used in the generation of
provenance, contributing with inferences to
discovering of implicit knowledge by means of
languages as RDF and OWL. This approach
provides as advantages the semantic description of
the context, improvements in queries and proofs of
origin and looking of interoperability of generated
data (Moreau et al, 2011).
In this work, time series provenance contributes
to the researcher to get information about the origin
and other characteristics of time series, helping and
facilitating the decision making about the use of
appropriate statistics procedures. In the following,
are presented four use cases involving real time
series data, which are related in Section 5.
- Use Case 1: in this case, it is important for the
researcher to known, by instance, if discrete
nonstationary time series presenting extreme events
such as outliers (Hair et al, 2010). This information
contributes to choose of an appropriate statistic
method for use, as a robust method (Chandler and
Scott, 2011).
- Use Case 2: another case is when the
researcher can identify the appropriate statistical
technique considering the observation type
(regularly or irregularly sampled). For analysis, the
autocorrelation function needs multiple pairs of
observations to quantify the serial dependence. In
this situation, the time series need to be regularly
spaced and with little bit of missing data. This
approach is not appropriate for observations in
intervals highly irregular, needing alternatives
techniques (Chandler and Scott, 2011).
- Use Case 3: also it is important to the
researcher to know the generator process and in
which statistic measure occurs the nonstationarity of
the time series, that is, in the mean or in the
variance. The nonstationarity in the mean can be
removed by differencing, for instance. However, in
inhomogeneous time series in the variance
(heteroscedastic time series), to reduce
nonstationarity, other transformations in the data are
needed (Wei, 2006).
- Use Case 4: another case is about the time
series decomposition model. This information
contributes to researcher to choose appropriate
statistical methods to trend removal of the time
series. For instance, if the time series were
decomposed additively (Yaffee and McGee, 2000),
the estimated trend is subtracted from data. To a
multiplicative decomposition model, this is done by
the division of time series by values of trend. In the
next section the ontology for time series provenance
is presented, developed as an OWL module.
5 ONTOLOGY FOR TIME
SERIES PROVENANCE
The methodology for development of domain
ontology is based on Ontology Development 101
(Noy et al., 2001). In parallel to this classic
methodology, the modularization of the ontologies
was considered (Suárez-Figueroa et al, 2012), where
ontologies are developed in separated parts, from the
self-contained form, being important to a sub-
domain or task, allowing scalability. Applied to
Ontology Engineering, modularity is central for
reducing the complexity of understanding and
maintenance, querying and reasoning over modules
(Kutz and Hois, 2012).
The modular design describes Time Series
Ontology (namespace tso:) related to time series
provenance and Detrend Ontology (namespace do:)
which describes statistical methods for trend
estimation. These modules (ontologies) are used in
the Detrend Provenance Model (namespace dpm:)
(De Souza et al, 2014) that reuse and extend the
Open Provenance Model - OPM (namespace opmo:)
(Moreau et al, 2011) as means of generating
semantic knowledge about detrending time series.
The Detrend Ontology and the Detrend Provenance
Model are not described in this paper.
It was identified, along with experts, a set of
competence questions that the ontology should be
able to answer, involving intrinsic features about
DomainOntologyforTimeSeriesProvenance
219
time series data and its components. They were
identified based on conceptual W7 Model (Ram and
Liu, 2009), which contributes to define, capture and
to use data provenance, presenting seven inter-
connected elements: What?, When?, Where?, How?,
Who?, Which? and Why?. These elements can be
used to track events that affect the data during its
lifetime. This provenance model is general and
extensible for capture provenance semantics for data
in different domains (Ram and Liu, 2009).
From these questions, the classes and its
relationships were identified, as well as the
instances. Restrictions on the classes and relations
are declared using axioms and/or rules, providing
semantics and allowing inferences by a reasoner in
the knowledge base. The elements from ontologies
are represented in this paper between parentheses.
The reuse from ontologies SWEET utilizes
namespaces of its sub-ontologies. For instance, the
subclass (phen:StochasticProcess) is declared as a
disjoint subclass of (tso:NonStochasticProcess). The
object property (rela:hasPhenomena) is reused and
(tso:hasDynamicalPhenomena) was created and
extended in (tso:hasStochasticProcess) and
(tso:hasNonStochasticProcess) which are declared as
disjoint properties.
The Time Series Ontology describes time series
related to nonstationary processes, which presenting
trends. These time series are the rule and are not the
exception in several application domains.
In relation to scope, are not included statistical
methods to transform the time series, which are
modeled in detrend module. About scalability, on
the one hand, the ontology is extensible due to reuse
of the triples from set of Ontologies SWEET, which
can be extended based on these ontologies.
The Classes Diagram developed in Ontograf
Plugin from Protégé 4.1, presents the main classes
related with the class (tso:TimeSeriesData) and the
respective provenance elements of W7 Model
(Figure 1). The classes represent the main
definitions and features of time series, including:
processes that generated them and time related;
analysis type associated and assumptions
considered; observation type done and how they can
be classified according to assumptions, knowledge
domain, collection, scientific instrument or generator
software related; models and types of decomposition
of time series and its components, as well as the
event component and the mathematical property
associated.
All classes are noted by means of the tag
(rdfs:comment), identifying which is the source of
the definition. This contributes to the understanding
of the concepts, as well as allows us to known which
is the provenance of the definitions. The data
properties and object properties are also noted by
means of this tag. Also the tag (rdfs:label) is used for
labeling the elements from this module.
The association of instances with DBpedia
resources allow, besides knowing its provenance,
obtaining more information about the data. This
way, it is possible to obtain semantic interoperability
about such concepts with LOD.
The ontology presents a classification as the
assumptions declared by means of defined rules.
Below some rules are presented that infers
knowledge about the time series.
tso:TimeSeriesData(?x),
tso:hasObservationType(?x,
tso:Regularly_Spaced) ->
tso:hasTimeSeriesAssumption(?x
,
tso:Homogeneity)
(1)
tso:TimeSeriesData(?x),
tso:hasTimeSeriesAssumption(?x
, tso:Homogeneity) ->
tso:hasObservationType(?x,
tso:Regularly_Spaced)
(2)
tso:TimeSeriesData(?x),
tso:hasTimeSeriesAssumption(?x
, tso:Homogeneity) ->
tso:HomogeneousTimeSeries(?x)
(3)
tso:TimeSeriesData(?x),
tso:hasTrendType(?x,
tso:Deterministic_Trend) ->
tso:NonStationaryTimeSeries(?x
)
(4)
The two first rules are related with the observation
type of time series (regularly or irregularly spaced)
and its classification, as the type of time series
related. If the observation is regularly spaced, the
time series are declared as presenting the
Homogeneity Assumption.
Also if the researcher declares that the time
series presenting the Homogeneity Assumption, they
are inferred how regularly spaced time series. The
opposite also occurs, when the observation is
irregularly spaced, the time series are inferred as
presenting the Heterogeneity Assumption.
According to third rule, if time series present the
Homogeneity Assumption, they are classified as
being of the type Homogeneous, belonging to class
(tso:HomogeneousTimeSeries). The same occurs
with the Heterogeneity Assumption.
When the time series presenting some type of
trend, for instance deterministic, according to fourth
rule, the same are inferred in the class
(tso:NonStationaryTimeSeries), where the trend
ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems
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Figure 1: TimeSeriesData Class and relationships with conceptual elements of the W7 Model.
component needs be extracted because it can hide
other phenomena, as well as the most statistical
methods are developed for stationary time series.
Figure 2 shows the extension from SWEET
Ontology related with the class
(phen:StochasticProcess), extended with the classes
(tso:NonStationaryProcess), (tso:StationaryProcess)
and its respective subclasses. According to a defined
rule, if the nonstationarity occurs in the mean and
the generator process of time series is considered
(tso: Stationary_Difference_Process), the inference
done is (tso:Stochastic_Trend). In the same way, if
the generator process of time series is
(tso:Stationary_Trend_Process), the inference upon
the trend type related is (tso:Deterministic_Trend),
done by Pellet reasoner (Sirin et al, 2007).
The information about the trend type is relevant
for the researcher to choose appropriate statistical
methods for detrending time series. In Figure 2(a),
the trend can be removed by Differencing, where the
same can be subtracted from time series. And in
Figure 2(b), the trend can be estimated by adjusting
of deterministic method as Regression Analysis that
fits a model to the trend, which is subsequently
removed from them.
Considering the Uses Cases (Section 4), Figure 3
presents a query about Use Case 1, showing which
nonstationary time series and its mathematical
property presenting some extreme event component.
Such knowledge contributes for the researcher to
choose statistical methods specifically developed for
these features as a robust method. The association of
the instances with DBpedia allows getting more
knowledge, besides contributing to semantic
interoperability.
About Use Case 2, Figure 4 shows features of
time series such as observation type, observation
interval and missing data percent. This knowledge
allows quantifying the autocorrelation function that
measures the dependence among sucessive
observations.
In Use Case 3 (Figure 5), the knowledge about in
which process and statistical measure the
nonstationarity occurs allows choosing an
appropriate method to extract it. About the Use Case
4 (Figure 6) describes about decomposition model,
bringing knowledge about the way as the trend can
be removed, in this case, by subtraction due to
additive decomposition model.
The ontology was evaluated by Ontologists and
Experts of time series area. For evaluation’s
applicability, were developed the following
documents: commitment term, describing the
purpose of the evaluation and about ethical
questions; list of competence questions; feedback
from evaluators about nomenclature, sources of
definitions and concordance in relation to the reuse.
The feedback from evaluators was analyzed and
considered in this module.
The semantic knowledge about time series
provenance, contributes meaningfully with the
analysis process, as the choice of appropriate
statistical methods that considers its characteristics.
DomainOntologyforTimeSeriesProvenance
221
Figure 2: TimeSeriesData class and its relationship with the phen:StochasticProcess class.
Figure 3: Features of nonstationary time series showing
extreme events, associated with DBpedia.
Figure 4: Observation type, missing data percent and
observation interval of time series.
6 RELATED WORKS
Henson et al (2009) presents an ontological
representation of time series observations for
Figure 5: Generator process and which statistical measure
the nonstationarity occurs in time series.
Figure 6: Model and type of Decomposition and
components related.
Semantic Sensor Web. It is described as time series
observations can be modeled in ontology, in order to
solve problems related to integration and queries.
This work is related to the modeling of observations
of time series from O&M XML Model. It is
presented as OWL allows data restrictions better
than XML, and also promotes semantic
ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems
222
interoperability. Nevertheless, this ontology
describes observations and measurements and does
not model intrinsic characteristics of time series.
The concept of semantic time series is defined by
Bozic (2011), where technologies from Semantic
Web are combined with time series processing
models, making possible its use in new applications.
However, this work proposes a generic language of
processing for simulation and modeling of the
semantic time series.
Other two works of the same author are Bozic
and Winiwarter (2013) and (Bozic and Winiwarter,
2012). The first is an extension of the second,
presenting a showcase about semantic time series
process. The showcase presents the functionality of
the Time Series Semantic Language (TSSL),
demonstrating as this technology can improve the
time series processing by the usage of a dedicated
language in a community building. This work shows
high practical impact in the time series process,
giving in new data source for applications of
semantic web.
Bozic and Winiwarter (2012) propose Time
Series Semantic Language – TSSL, a generic
community building language for semantic time
series, allowing observing data flux as data sensor
with additional information, tagging postings of
scientists with a specific search topic. The TSSL
architecture supports high level of expressivity, user-
friendly syntax, extensibility, allowing significant
data models. It presents the Time Series Processor -
TSP, which coordinates all workflow process of
time series. The main contribution of this paper is
the semantic time series processing, related to time
series data and also its meaning, creating new
information by means of links among different data
structures.
Comparing with related works, the same do not
describe intrinsic features of time series data. The
OWL module proposed in this work can be extended
and contributes to the researcher to know and
understanding better the data (time series),
facilitating the decision making about as turn them
stationary, improving semantically an important step
of preprocessing phase of time series analysis that is
the trend extraction.
7 CONCLUSIONS
The scientific contribution of this paper presents two
aspects. First, about ontology engineering, is
presented a study of case related to modular design
of ontologies, presenting the development of a
module related to time series provenance, developed
by separated way of related statistical procedures.
In this case, the modularity decrease the
modeling complexity, facilitate individual
evaluation, promoting the reuse and extensibility of
modules. Another contribution of this nature is the
generation of provenance information for a special
type of data, characterized by showing temporal
dependence of observations. Also, the definition of
the competence questions using expressions of the
W7 model, contribute to obtain knowledge about
time series provenance.
Second, the contribution that stands out is in time
series area, enriching them semantically, improving
the analysis process, facilitating the decision making
about appropriate statistical procedures and
contributing for the scientific knowledge generation.
The applicability of proposal domain ontology is
related with nonstationary time series, which
presenting trends. In development of ontology, was
considered the orthogonality of concepts, where the
same are decomposing in its components parts,
facilitating its extensibility.
The proposal ontology presents as main
advantages: the generation of provenance
information about time series; the reuse of
statements from set of Ontologies SWEET, allowing
semantic interoperability and extensibility; the
definition of classes using nomenclature from
bibliographies of time series analysis, contributing to
the understanding of concepts, which can be
visualized by an online documentation developed;
the association, when applicable, of the instances
with DBpedia enables to increase the ontology
definitions and contributes for semantic
interoperability with linked open data; and the use of
rules allows to infer more semantic knowledge. The
ontology also contributes to the choice of the
appropriate statistical methods, facilitating the
decision making in detrending step.
With the modular development is necessary to
select subject for module composition. In this work,
data and methods are considered as separated
modules, which are combined in the detrend
provenance model. Also, in this context, stands out
that the wide range of time series analysis area turns
it difficult the understanding about concepts and its
relationships.
The main contribution of this paper is based on
intersection of the following key topic of search:
time series and its components, provenance,
ontologies and the semantic web, resulting in the
generation of domain ontology for time series
provenance, as a means to enrich them semantically,
DomainOntologyforTimeSeriesProvenance
223
allowing logic inferences and the development of
queries.
As future works stands out the development of
an online environment using the proposal ontology,
contributing to facilitate and enrich semantically the
trend extraction step of preprocessing phase of the
time series analysis.
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