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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>H. Yao, A.M. Orme, L. Etzkorn, Cohesion Metrics for Ontology Design and Application, J. of
Computer Science</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Metrics In The NEOntometrics Application</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Achim Reiz</string-name>
          <email>achim.reiz@uni-rostock.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kurt Sandkuhl</string-name>
          <email>kurt.sandkuhl@uni-rostock.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>NEOntometrics</institution>
          ,
          <addr-line>Ontology Metrics, Knowledge Graph, Quality Management</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Rostock University</institution>
          ,
          <addr-line>18051 Rostock</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2023</year>
      </pub-date>
      <volume>1</volume>
      <issue>2005</issue>
      <fpage>229</fpage>
      <lpage>233</lpage>
      <abstract>
        <p>Metrics offer an objective assessment of the inner fabrics of ontologies. They allow us to quickly understand graph properties, logical complexity, completeness of human-centered annotations, or degree of interconnection. When analyzed historically, ontology metrics tell much about development decisions and the impact of changes and can be used for quality control measures. The NEOntometrics software allows calculating evolutional ontology metrics for git-based repositories and implements the majority of literature-proposed metric frameworks. This paper presents the recently added visualization capabilities for visualizing the differences between ontologies in a repository, assessing the change impact of the most recent commit, and examining ontology evolution.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        recommendation systems [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], or autonomous driving [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. They build on subsets of first-order logic,
which has little in common with traditional data
modeling or imperative programming. The
development team is often dispersed skill-wise, experience-wise, in their responsibilities, and
geographics [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. The complexity and collaborative development processes put quality control activities
at the forefront. Users and ontology managers need to understand the impact of proposed changes and
the evolutional history of the artifacts as a whole to make informed development decisions.
      </p>
      <p>One way to gather these kinds of information is the calculation of metrics. Ontology metrics translate
the structural attributes of ontologies into objective, reproducible measurements. The measures cover
the use of RDF(S) and OWL formalisms, graph properties, or human-centered annotations.</p>
      <p>
        With NEOntometrics [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], a tool is available for analyzing large amounts of historical metric data
based on git repositories. NEOntometrics implements most proposed ontology metrics and allows csv
data export or integration into custom applications and analyses using a GraphQL interface. Until
recently, however, the frontend visualization capabilities were limited to a tabular metric representation.
      </p>
      <p>This paper presents a new integrated visualization feature for NEOntometrics. The evolutional
developments and the differences of ontologies in a repository can now be displayed using diagrams.
A comparison view for the last two versions of an artifact visualizes changed measures, thus allowing
a quick overview of impacted structural attributes. Integrating diagram capabilities into software for
calculating ontology metrics eases the consumption and productive use of the measures and hopefully
contributes to the broader dissemination of ontology metrics for quality control.</p>
      <p>The paper is structured as follows: The next section recapitulates the state of the art regarding
ontology evolution and visualization approaches. Section three presents NEOntometrics, including the
newly implemented visualization features. The research concludes with an outlook and a discussion.</p>
      <p>
        2023 Copyright for this paper by its authors.
[
        <xref ref-type="bibr" rid="ref11 ref12">11,12</xref>
        ]
      </p>
      <p>
        #
[
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]
[
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]
[14]
[15]
[16]
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        In this related work, we aim to recapitulate the current state regarding software support for ontology
evolution and evolution visualization. [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] further contains a review of software support for ontology
metric calculation. Hence, it is not thoroughly discussed in this paper.
      </p>
      <p>Analyzing and visualizing ontology evolution is a multifaceted field with various manifold
approaches. As such, there are already extensive literature reviews that collected the relevant state of
the art:</p>
      <p>
        Novais et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] collected an extensive review of visualization approaches in the related field of
software evolution and classified the existing research (among others) along their application scenarios,
visual paradigms and attributes, data sources, and explanation strategy.
      </p>
      <p>
        Lambrix et al. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] collected software for ontology and software evolution and categorized them along
their functionality, which is further assigned to evolution steps and change categories. De Leenheer and
Mens [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] presented processes and tool support for single-developer and collaborative ontology
development processes. They focus on the challenges of inter-organizational changes with multiple
possible ontology managers and the corresponding organizational requirements. These authors also
present their own collaborative ontology engineering process DOGMA, including tool support [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
Tudorache [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] recapitulated the recent advances in ontology engineering, including software support.
While she argues that the tool support is nowadays much better suited not only for research but also for
commercial projects, she also argues for making access easier for newcomers and for increasing the
usability of the tools.
2 https://github.com/dbs-leipzig/conto_diff – Only the underlying algorithm of CODEX is open source
3 https://github.com/rsgoncalves/ecco/
4 https://github.com/psiotwo/owldiff
5 https://gitlab.ifi.uzh.ch/DDIS-Public/chimp-protege-plugin
6 https://github.com/NJITSABOC/oaf-protégé – no license attached
      </p>
      <sec id="sec-2-1">
        <title>Dogma Studio</title>
      </sec>
      <sec id="sec-2-2">
        <title>Standalone</title>
      </sec>
      <sec id="sec-2-3">
        <title>Type</title>
      </sec>
      <sec id="sec-2-4">
        <title>Standalone</title>
      </sec>
      <sec id="sec-2-5">
        <title>Standalone, API</title>
      </sec>
      <sec id="sec-2-6">
        <title>Shell</title>
      </sec>
      <sec id="sec-2-7">
        <title>Protégé Plugin</title>
      </sec>
      <sec id="sec-2-8">
        <title>Standalone,</title>
      </sec>
      <sec id="sec-2-9">
        <title>Protégé Plugin</title>
      </sec>
      <sec id="sec-2-10">
        <title>Protégé Plugin</title>
      </sec>
      <sec id="sec-2-11">
        <title>Protégé Plugin</title>
      </sec>
      <sec id="sec-2-12">
        <title>Use case</title>
      </sec>
      <sec id="sec-2-13">
        <title>Identify and visualize unstable ontology regions</title>
      </sec>
      <sec id="sec-2-14">
        <title>Understand and visualize ontology changes and their impacts</title>
      </sec>
      <sec id="sec-2-15">
        <title>Detect changes between two ontology versions</title>
      </sec>
      <sec id="sec-2-16">
        <title>Comparing Structural changes</title>
        <p>between two ontology versions</p>
      </sec>
      <sec id="sec-2-17">
        <title>Compare and merge two OWL2 ontologies</title>
      </sec>
      <sec id="sec-2-18">
        <title>Dashboard view of evolved ontology metrics</title>
      </sec>
      <sec id="sec-2-19">
        <title>Manage ontology evolution in</title>
        <p>collaborative environments</p>
      </sec>
      <sec id="sec-2-20">
        <title>Summarizes the changes in taxonomical view Available</title>
        <p>❌
❌
❌
❌
✅
✅
❌
✅</p>
      </sec>
      <sec id="sec-2-21">
        <title>Open Source</title>
        <p>❌
✅2
✅3
❌
✅4
✅5
❌
(✅)6
unstable ontology subparts. To instantly understand the impact of modeling decisions in the Protégé
editor, [17] calculates a taxonomy of changes, and [16] calculates numerical differences between the
saved version and currently performed changes.</p>
        <p>While the visualization view of the new NEOntometrics features (cf. Figure 4) has some similarities
to [16], our approach does not calculate the metrics instantly for a change but regards the last two
committed versions in a git repository. NEOntometrics also implemented a more significant number of
ontology metrics, allowing us to choose from ~160 metrics from different frameworks. Compared to
the current state of the art regarding tool-supported ontology evolution, the NEOntometrics approach is
strictly focused on visualizing ontology metrics. Further, it not only regards two versions but calculates
and visualizes the overall version history, thus allowing conclusions on overall evolutional processes
and design decisions.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. NEOntometrics</title>
      <p>
        NEOntometrics is a web-based application that calculates evolutional ontology metrics of git-based
repositories. It iterates through a repository and calculates the respective measures for every ontology
in every commit if the file has changed. It comes with an interactive help page Metric Explorer, is open
source7, and is available online8. For more information on NEOntometrics, cf. [
        <xref ref-type="bibr" rid="ref4">4,18</xref>
        ].
      </p>
      <p>As calculating the version history of ontology repositories can take a considerable amount of time,
NEOntometrics works asynchronously. A new calculation can be triggered by pasting the URL to a
given repository in the bottom text field of the Calculation Engine (cf. Figure 1). If the repository is not
yet known to the system, it can be put in the calculation queue. Afterward, a separate worker application
retrieves the ontology from the git repository and starts the analysis.</p>
      <p>The ontology metrics can be retrieved as soon as the calculation is finished. Currently,
NEOntometrics supports OQuaRE [19], OntoQA [20], oQual [21], the cohesion metrics by Yao et al.
[22], the good ontology metrics by Fernández et al. [23], Orme et al.’s evolutional metrics [24], and the
complexity metrics by Yang et al. [25]. Metrics can be run on the ontology as it is or on the inferred
graph. However, as the inference engine can take a considerable time, it is only advised for small
ontologies.
7 https://github.com/achiminator/NEOntometrics
h http://neontometrics.com</p>
      <p>After selecting the desired metrics and frameworks and triggering the retrieval process, the software
shows a paginated tabular view of the ontology metrics. The button “show the analytic” opens the
visualization page. The measures shown in the diagrams are always congruent to the ones selected
during the ontology retrieval process.</p>
      <p>Three visualizations are available to examine the most recent changes, compare ontologies in a
repository, and visualize the ontology evolution. The figures below exemplify these visualizations for
the SciData ontology9 for interoperable scientific data exchange [26].</p>
      <p>The first chart (cf. Figure 2) displays differences between the repositories’ ontologies in a bar
diagram. The bar diagram presents the last version of each ontology. It allows a quick comparison of
the available artifacts in a repository. The diagram can be scrolled by dragging the picture to either side
of the frame. Hovering over a measure shows the detailed measures. Ontologies can be selected and
deselected by clicking on their name below the chart. The scaling changes dynamically depending on
the sizes of the bars visible in the frame.</p>
      <p>The bar chart in the example visualizes the axioms and classes of the repositories’ ontologies. The
thermo, scidata, and cao files have the most classes and axioms. However, cao has many more axioms
than thermo. Thus, one can conclude that the thermo ontology is more driven by a taxonomical class
structure, while scidata and cao have more additional axioms than thermo.</p>
      <p>Further examination revealed that cao and scidata are indeed more logically interconnected. In the
given example, the bar chart visualizes discrete count-based measures. However, the bar chart
visualization works also for ratio-based formulas. For example, the OntoQA metrics shown in Table 2
and visualized in the line chart in Figure 3 could also be used in the bar diagram.</p>
      <p>The second visualization (cf. Figure 3) contains an evolutional view of one ontology for the selected
ontology metrics. It allows an understanding of the impact of changes on the structural attributes and
can be used to understand and evaluate design decisions. The drop-down menu at the top of the window
changes the ontology to be visualized. The user can activate and deactivate measures by clicking their
name on the legend below the chart, and the diagram scales automatically, similar to the bar chart.
Hovering over a data point gives further details on the displayed value.</p>
      <p>The diagram in Figure 3 shows four OntoQA measures for the scidata ontology. At first, it is evident
that relationship diversity is constantly at 0, originating from the fact that no object properties are
declared on classes. The class utilization and average population increase early in the lifetime of the
ontology. Otherwise, they stay reasonably consistent. No individuals nor classes were added in this
ontology, and the changes in classes and the subclass structure are relatively subtle. On the opposite,
9 https://github.com/stuchalk/scidata - The authors of SciData and this paper are not affiliated with each other.
the attribute richness increases heavily. As the classes are somewhat consistent, these changes are driven
by data and object properties. Also, the ontology describes a relatively high number of data and object
properties compared to declared classes.</p>
      <sec id="sec-3-1">
        <title>Attribute Richness</title>
      </sec>
      <sec id="sec-3-2">
        <title>Average Population</title>
      </sec>
      <sec id="sec-3-3">
        <title>Relationship Diversity</title>
      </sec>
      <sec id="sec-3-4">
        <title>Class Utilization</title>
        <p>Calculation</p>
        <p>The last analysis shows which measures have changed and by how much in the recent commit. It
thus provides a detailed view of the ontologies’ last two versions and shall allow a quick assessment of
the impact of the most recent change to evaluate the usefulness and identify eventually unintended
sideeffects. Similar to the previous analysis, the ontology can be selected in the drop-down menu at the top
of the application. In contrast to the other visualizations, this view shows not only the selected metrics
but every metric that has changed. The little icon on the left indicates an increase (⬆️ ) or decrease
(⬇️ ). If a metric does not change, it is not on the list.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion</title>
      <p>The evolutional analysis of ontology metrics offers an objective insight into the evolvement of their
structural attributes and can tell much about underlying design decisions. With the software
NEOntometrics, tool support is available for analyzing large quantities of ontologies. The new
visualization capabilities presented in this paper extend the application for an easily consumable
humanoriented metric interface. We hope they ease the consumption of ontology metrics and contribute to a
broader dissemination of metrics for quality control.</p>
      <p>Application for the ontology metrics are manifold. For example, the metrics allow the user to
understand evolutional processes or differences between various ontologies. Ontology metrics can aid
in making better-informed reusing and development decisions as they allow quickly grasping an
ontology’s inner fabrics. One can set objective and reproducible goals for ontology developments and
track their achievement through metrics.</p>
      <p>Soon, we plan on integrating even more visualization capabilities to allow a better deep dive into
the ontology development processes. Further on the NEOntometrics roadmap is integrating more
ontology metrics, e.g., to assess SHACL-constructs and use of custom vocabularies. In that sense, we
are interested in the functionalities that the community would like to see implemented. A potential
evaluation of the usefulness of the visualizations and metrics is also desirable in future work.</p>
    </sec>
    <sec id="sec-5">
      <title>5. References</title>
    </sec>
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