<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>TOMATO: results of the 2024 OAEI evaluation campaign</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Philippe Roussille</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olivier Teste</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>École 3iL</institution>
          ,
          <addr-line>Limoges</addr-line>
          ,
          <institution>Institut de Recherche en Informatique de Toulouse</institution>
          ,
          <addr-line>Toulouse</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Université Toulouse 2 Jean Jaurés, Institut de Recherche en Informatique de Toulouse</institution>
          ,
          <addr-line>Toulouse</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>This paper presents the results obtained by TOMATO in the OAEI 2024 evaluation campaign. We describe here the results in the Conference track and our first . We report a general discussion on the results and future improvements of the system.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Presentation</title>
      <sec id="sec-1-1">
        <title>1.1. Overview</title>
        <p>
          TOMATO (TOolkit for MATching Ontologies) takes inspiration from previous work on ontology
matching systems such as POMAP++ [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. TOMATO is designed as a pairwise matcher, aligning
pairs of input ontologies against each other. At its core, TOMATO utilizes machine learning
approaches to learn from element similarities. In earlier versions, it focused mainly on
stringbased similarity measures of ontology elements [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          Challenges in Previous Versions. Earlier iterations of TOMATO, such as the 2023 system
[
          <xref ref-type="bibr" rid="ref3">3</xref>
          ], heavily relied on reference alignments for training machine learning models. This
dependency led to issues of overfitting and limited generalizability when applied to new datasets.
Furthermore, the lack of external ground truth for most OAEI tracks posed a challenge to
developing robust machine learning approaches.
        </p>
        <sec id="sec-1-1-1">
          <title>Shift Towards Machine Learning and Scalable Alignment. In 2024, TOMATO made</title>
          <p>significant strides by shifting towards a more machine learning-centric approach while
minimizing dependency on reference alignments. However, the challenge remains: how can machine
learning models be trained without a reliable ground truth? To address this, several strategies
were explored:
• Artificial Alignment Generation . Leveraging large language models (LLMs) such as
ChatGPT and XLM-Roberta, we generated hypothetical alignments between ontology
entities, which were used to train models without relying on reference alignments.
• Exploring Alternative Model Architectures. To better interpret the learned
alignment patterns, we experimented with models such as Decision Trees. These models
provided insights into the significance of various similarity metrics, but faced limitations
in generalizing across ontologies.
• Self-Alignment as a Baseline. A quick and practical solution was self-alignment, where
an ontology was aligned with itself. This allowed us to generate accurate correspondences,
which improved precision but led to a drop in recall due to a lack of variability.</p>
        </sec>
      </sec>
      <sec id="sec-1-2">
        <title>1.2. Workflow</title>
        <p>The workflow in TOMATO begins by taking as input two OWL ontologies to be aligned,
along with their associated reference RDF alignment files. These reference alignments provide
examples of entity matches that serve as ground truth for the learning process.</p>
        <p>TOMATO then prepares the data by combining all ontology entity pairs (both matched and
unmatched based on our training data) into a single dataset. This set contains all possible entity
couples across the input ontologies, along with their reference match status.</p>
        <p>From here, TOMATO can be used in one of two modes:
1. Learning mode: A machine learning model is trained on the full mixed dataset to learn
the patterns of matching vs non-matching entities.
2. Matching mode: A pre-trained model is applied to new ontology entity pairs to predict
their alignment status.</p>
        <p>Unlike previous versions where we explored a wide range of similarity measures, our focus this
year has shifted toward finding ways to train models without relying on reference alignments.
This change stems from the recognition that reference alignments, while useful, introduce
biases that may limit the generalization of the system to unseen ontologies.</p>
        <p>In 2024, our approach centers on the development of alternative strategies for generating
training data, such as creating artificial alignments using large language models and leveraging
self-alignment techniques. These methods provide the system with diverse examples of both
trivial and complex matches, allowing it to learn general alignment patterns without depending
on explicit reference data. This way, TOMATO is able to explore a broader spectrum of alignment
examples, improving its robustness and adaptability to various ontology domains.</p>
      </sec>
      <sec id="sec-1-3">
        <title>1.3. Matching steps</title>
        <p>The initial step in TOMATO’s workflow is to parse and ingest the input ontologies. We leverage
the owlready2 Python library to build an in-memory representation containing all ontology
elements and relationships.</p>
        <p>Each entity such as classes, data properties and object properties is indexed via a unique
identifier, with the preferred identifier being the element’s label if present. As a fallback, the
ifnal segment of the entity’s URI is used.</p>
        <p>Structural relationships between classes are also extracted and stored. This includes
superclasssubclass links as well as relations defined through object properties.</p>
        <p>By fully populating an internal graph structure in this way, TOMATO is able to consider
both lexical properties of entities as well as their positions and connections within the ontology
taxonomy during the matching process. This combined view aims to capture more
contextual evidence about intended semantic correspondence compared to considering elements in
isolation.</p>
        <p>The loaded ontologies can then be queried as needed during the various steps of similarity
computation, model training and alignment prediction.</p>
        <sec id="sec-1-3-1">
          <title>1.3.1. Ontology Preprocessing</title>
          <p>As in prior iterations, we apply standard text preprocessing techniques to clean and normalize
entity labels before computing similarities. This includes:
• Converting CamelCase to snake_case
• Replacing non-alphanumeric symbols with spaces
• Performing English stemming
• Removing stop words</p>
        </sec>
        <sec id="sec-1-3-2">
          <title>1.3.2. Train and match</title>
          <p>Training a Model. We have shifted our focus this year from relying on reference alignments to
training our models using alternative methods. Instead of using predefined reference alignments
to label entity pairs as matches (1) or non-matches (0), we now generate training data by aligning
an ontology with itself. This ensures a perfect match for all entities, providing a reliable ground
truth.</p>
          <p>In this approach, we construct a similarity matrix for the ontology pair by comparing an
ontology to itself. This matrix is then fed into a pre-trained matching model, which is now
based on self-alignment data. By using an ontology’s internal structure to generate matches,
we aim to create robust training examples that improve the model’s ability to generalize across
diferent ontologies.</p>
          <p>Computing Alignments. A similarity matrix is constructed for the target ontology pair.
This matrix is then input to the pre-trained matching model, which outputs the predicted entity
alignments.</p>
          <p>This year, we successfully broke a significant barrier regarding memory usage by optimizing
the overall memory footprint of the system. Through careful optimization of the internal data
structures and eficient management of the similarity matrix, we were able to substantially
reduce the memory requirements. This allowed TOMATO to handle larger and more complex
ontologies without encountering memory overloads, an issue that had previously limited our
participation in certain OAEI tracks.</p>
          <p>However, despite these improvements, there remain some unresolved issues, likely related
to how Docker is used internally for managing the computational processes. These issues
occasionally result in suboptimal performance, particularly when handling very dense or highly
interconnected ontologies. Despite these challenges, we were still able to successfully participate
in the Anatomy Track for the first time, demonstrating the robustness of TOMATO’s alignment
capabilities.</p>
          <p>By optimizing memory usage and tackling system scalability, we have made significant
progress in improving TOMATO’s overall performance. Nevertheless, addressing the remaining
Docker-related issues is a key area for future development.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. The problem for ground truth</title>
      <sec id="sec-2-1">
        <title>2.1. Generating Artificial Alignments with Large Language Models</title>
        <p>One of the first strategies we explored was the generation of artificial alignments using large
language models (LLMs) such as ChatGPT and XLM-Roberta. The idea behind this approach
was to leverage the capabilities of these advanced models to produce hypothetical alignments
between ontology entities, while explicitly excluding reference alignments provided by the
OAEI.</p>
        <p>
          As demonstrated by He et al. [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ], large language models are capable of identifying semantic
relationships between terms, but they struggle with the complexities of specialized terminologies
and structures found in ontologies.
        </p>
        <p>The goal was to generate plausible correspondences that could serve as training data for our
machine learning models. By excluding the reference alignments, we aimed to address the issue
raised in previous OAEI campaigns regarding the use of such resources. Large language models,
trained on vast amounts of text data, are capable of identifying semantic relationships between
terms, and we hoped to capitalize on this ability to create a diverse set of alignment examples.
Challenges Encountered. However, this approach quickly revealed several significant
challenges. First and foremost, the size, structure, and exhaustive nature of ontology descriptions
had a direct impact on the performance of the LLMs. Ontologies often consist of highly
specialized terminology, complex relationships, and formal structures, which LLMs may struggle to
accurately interpret or generate.</p>
        <p>The quantity and form of ontology descriptions – whether detailed or concise—heavily
influenced the quality of the alignments produced. In some cases, the artificial alignments
generated by the models were too generic or semantically incorrect, lacking the necessary
precision to serve as useful training data. This issue was exacerbated by the complexity of
ontological relationships, such as hierarchical structures and role-based associations, which
LLMs failed to capture consistently.</p>
        <p>As a result, the alignments we produced with this method quickly proved to be unusable
for training purposes. The generated correspondences either did not align with the real-world
complexity of ontology matching or introduced too much noise, rendering them inefective for
model learning.</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Exploring Alternative Model Architectures</title>
        <p>In parallel to generating artificial alignments, we explored alternative machine learning model
architectures to address the issue of not relying on reference alignments. Our primary approach
was to experiment with models such as Decision Trees, which ofer a more interpretable
representation of the matching process. The goal of this approach was to better understand the
importance of diferent similarity measures and how they contribute to successful alignments.</p>
        <p>
          Decision Trees ofer interpretable alignment models, as highlighted in Fleissner et al. [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ] and
Kokash et al. [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ], where the use of Decision Trees for clustering and alignment tasks is explored.
        </p>
        <p>By using models like Decision Trees, we aimed to generate explicit rules that could guide the
alignment process. Unlike black-box models, such as neural networks, Decision Trees provide
clear decision paths, allowing us to analyze how various similarity metrics—lexical, structural,
and semantic—are weighted and applied to diferent types of correspondences (e.g., class vs.
property alignments).</p>
        <p>Challenges Encountered. While Decision Trees ofered greater interpretability, they also
introduced several challenges. First, the complexity of ontology alignment often exceeds the
capacity of simple rule-based models. Ontologies involve intricate hierarchical structures,
multiple types of relationships, and a high degree of semantic ambiguity, all of which are
dificult to capture with rigid, predefined rules.</p>
        <p>As we tested this approach, it became clear that Decision Trees struggled to generalize across
diferent ontologies. The alignment rules generated were often specific to the training data
and did not perform well when applied to new, unseen ontologies. In addition, the depth
and complexity of the trees quickly escalated as we introduced more features and similarity
metrics, leading to overfitting. This overfitting resulted in poor generalization and a lack of
robustness when the model encountered ontologies with diferent structures or domain-specific
terminologies.</p>
        <p>Although this approach provided valuable insights into the role of various similarity measures,
it ultimately highlighted the need for more flexible models capable of handling the nuanced and
complex nature of ontology alignment. Despite the limitations, the experiment underscored
the importance of better feature selection and the need for hybrid approaches that combine
rule-based reasoning with more adaptive learning techniques.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Self-alignment as a quick-and-dirty solution, which ultimately worked</title>
        <p>As a rapid solution to the training problem, we implemented an approach where the system
aligns an ontology with itself. This method was introduced as a quick workaround to avoid
using reference alignments, while still providing a baseline for the machine learning model to
learn from. The self-alignment ensures that all correspondences between entities are correct by
design, as they involve the same ontology being aligned to itself.</p>
        <p>Initial Results. During testing, we found that this method allowed us to maintain an
acceptable level of precision, although it led to a noticeable drop in recall. Since the system was trained
on perfect correspondences (i.e., each entity aligning with itself), it struggled to generalize to
more complex inter-ontology alignments, where correspondences are less obvious or more
semantically intricate.</p>
        <p>Despite this drop in recall, the precision remained high, as the system could accurately identify
correct matches within the self-alignment framework. The key insight from this experiment
is that while recall sufers due to the lack of variability in the training data, precision can
be maintained in a controlled environment. This suggests that the model still benefits from
understanding simpler correspondences, which may serve as a foundation for more complex
learning in future iterations.</p>
        <p>Ongoing Use of This Approach. Given the stability of the precision, we decided to retain
this approach for the time being, using it as a foundational method while exploring other
strategies for improving recall. We maintained the same  parameter configuration as last
year, which controls the balance between positive and negative examples during training. This
allowed us to keep the same level of precision while investigating ways to enrich the model’s
ability to capture more complex correspondences.</p>
        <p>This approach has also proved useful in reinforcing the insights gained from the first two
strategies. In particular, it has highlighted how the generation of artificial noise and the
exploration of diferent model architectures can help refine the system’s overall alignment
capabilities. Moving forward, we plan to combine self-alignment with other techniques, such
as artificial alignment generation and feature-driven model exploration, to further enhance
TOMATO’s performance.
TOMATO participated again this year in the Conference Track of the OAEI, where the objective
is to align academic domain ontologies. The Conference Track remains a key environment
for evaluating matching systems, as it involves dense and diverse ontologies that represent
concepts and relationships within academic contexts, such as publications, authors, conferences,
and institutions.</p>
      </sec>
      <sec id="sec-2-4">
        <title>3.1. Raw results</title>
      </sec>
      <sec id="sec-2-5">
        <title>3.2. Comparison</title>
      </sec>
      <sec id="sec-2-6">
        <title>3.3. Overall Performance</title>
        <p>In 2024, TOMATO showed a slight decrease in performance compared to the previous year. The
F-measure dropped from 0.52 in 2023 to 0.49 this year, mainly due to a drop in recall, which
went from 0.47 to 0.43. Precision, however, remained stable at 0.57, indicating that TOMATO
continues to produce accurate alignments, though with reduced coverage, i.e., fewer relevant
correspondences are being found.</p>
      </sec>
      <sec id="sec-2-7">
        <title>3.4. Comparison with 2023</title>
        <p>Compared to last year’s results, TOMATO’s recall decreased, contributing to the overall drop in
the F-measure. However, it is worth noting that TOMATO maintained a good precision score,
demonstrating that the correspondences it does identify tend to be correct. This stability in
precision is encouraging, as it suggests a solid foundation that can be built upon by improving
recall in the future.</p>
      </sec>
      <sec id="sec-2-8">
        <title>3.5. Approach and Future Directions</title>
        <p>This year, the primary focus for TOMATO was on avoiding the use of reference alignments for
model training, addressing concerns raised in the previous OAEI campaign. Despite this shift,
TOMATO managed to maintain a consistent precision, although the recall dropped slightly due
to the exclusion of reference alignments from the training process.</p>
        <p>Looking ahead, we aim to improve TOMATO’s recall by incorporating external knowledge
sources, such as knowledge graphs, to capture more complex and subtle correspondences.
Further experimentation with hybrid strategies combining machine learning with
heuristicbased matching could also enhance TOMATO’s performance on large-scale, diverse ontology
matching tasks.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>4. Results of the OAEI 2024 Anatomy Track</title>
      <p>TOMATO participated for the first time in the Anatomy Track, which involves aligning the
Adult Mouse Anatomy with a section of the NCI Thesaurus representing human anatomy. This
track presents unique challenges due to the large size and technical complexity of the ontologies
involved. These ontologies are meticulously designed and contain highly specialized terms.
Furthermore, they difer from other ontologies in their use of specific annotations and roles,
such as the extensive use of the partOf relation.</p>
      <sec id="sec-3-1">
        <title>4.1. Performance and Challenges</title>
        <p>TOMATO’s performance on the Anatomy Track was moderate, placing it behind established
systems like LogMap and Matcha in terms of F-measure and recall. The following table summarizes
TOMATO’s performance compared to other systems:</p>
        <p>TOMATO achieved a precision of 0.955, which is among the highest in the track. However,
its recall was significantly lower at 0.36, leading to a moderate F-measure of 0.523. The low
recall indicates that TOMATO struggled to capture a large number of relevant correspondences,
especially non-trivial matches. In terms of recall+, which measures non-trivial correspondences
(i.e., those that do not have identical labels), TOMATO’s performance was the lowest in the
track (0.024).</p>
        <p>One key limitation observed during this evaluation was related to memory usage and
execution speed. The ontologies in the Anatomy Track are not only large but also structurally
complex, which increases the computational demands during the alignment process. Despite
eforts to optimize TOMATO’s performance, we encountered memory bottlenecks and execution
times that exceeded acceptable thresholds, particularly when dealing with large datasets.</p>
      </sec>
      <sec id="sec-3-2">
        <title>4.2. Areas for Improvement</title>
        <p>The Anatomy Track highlights several areas where TOMATO needs improvement.
• Memory management. The large size of the ontologies, coupled with their detailed
conceptualization and numerous annotations, requires a more eficient use of memory.
Current limitations have led to performance bottlenecks, particularly when processing
the full scope of the anatomy ontologies.
• Execution speed. Given the complexity of the relationships in these ontologies, such
as the extensive use of the partOf relation, TOMATO’s runtime has proven slower than
expected (2154 seconds). We need to further optimize the system to handle these large,
hierarchical structures more eficiently.</p>
        <p>Despite these challenges, TOMATO has demonstrated its potential in managing simpler
correspondences, and we are confident that with improved memory handling and speed
optimizations, it can perform more competitively in future Anatomy Track evaluations. Future
work will focus on reducing computational overhead while maintaining the precision levels
observed during this year’s evaluation.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>5. Conclusion and Future Directions</title>
      <p>This work highlights the key challenges associated with applying machine learning (ML)
approaches to ontology matching, particularly in the absence of a reliable ground truth. Unlike
traditional matching systems, ML models rely heavily on training data to learn patterns of
similarity between entities. The lack of a dedicated ground truth complicates this process, as
generating accurate and unbiased training examples becomes a significant hurdle. In the OAEI
context, the prohibition against using reference alignments for training further exacerbates this
issue, leaving ML-based systems like TOMATO at a disadvantage compared to heuristic-based
systems.</p>
      <p>However, in certain tracks, such as the medical ontologies, this challenge could be mitigated
by leveraging external knowledge sources. Medical ontologies, for instance, benefit from large,
well-established resources like SNOMED CT and the Unified Medical Language System (UMLS),
which provide robust, validated knowledge bases that could serve as a proxy for ground truth. By
incorporating such external resources, ML-based approaches could be trained more efectively,
leading to more accurate and generalized matching results in those domains.</p>
      <p>We plan to integrate clustering-based noise generation with our existing strategies to improve
TOMATO’s performance. In addition, exploring the use of external knowledge bases in tracks
where they are available (e.g., medical ontologies) could provide a more stable ground for
training ML models. Finally, we will continue refining the feature selection process and hybrid
approaches, combining rule-based reasoning with ML, to address the inherent complexity of
ontology alignment tasks.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>A.</given-names>
            <surname>Laadhar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Ghozzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I.</given-names>
            <surname>Megdiche</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Ravat</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Teste</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Gargouri</surname>
          </string-name>
          , POMap++
          <article-title>results for OAEI 2019: fully automated machine learning approach for ontology matching</article-title>
          ,
          <source>in: 14th International Workshop on Ontology Matching co-located with the International Semantic Web Conference (OM@ISWC</source>
          <year>2019</year>
          ), Auckland, New Zealand,
          <year>2019</year>
          , pp.
          <fpage>169</fpage>
          -
          <lpage>174</lpage>
          . URL: https://hal.archives-ouvertes.fr/hal-02942337.
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>M.</given-names>
            <surname>Cheatham</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Hitzler</surname>
          </string-name>
          ,
          <article-title>String similarity metrics for ontology alignment</article-title>
          , in: H.
          <string-name>
            <surname>Alani</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          <string-name>
            <surname>Kagal</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Fokoue</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          <string-name>
            <surname>Groth</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          <string-name>
            <surname>Biemann</surname>
            ,
            <given-names>J. X.</given-names>
          </string-name>
          <string-name>
            <surname>Parreira</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          <string-name>
            <surname>Aroyo</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          <string-name>
            <surname>Noy</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          <string-name>
            <surname>Welty</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          Janowicz (Eds.),
          <source>The Semantic Web - ISWC 2013</source>
          , Springer Berlin Heidelberg, Berlin, Heidelberg,
          <year>2013</year>
          , pp.
          <fpage>294</fpage>
          -
          <lpage>309</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>P.</given-names>
            <surname>Roussille</surname>
          </string-name>
          ,
          <string-name>
            <surname>O. Teste,</surname>
          </string-name>
          <article-title>TOMATO : results of the 2023 OAEI evaluation campaign</article-title>
          ,
          <source>in: 18th International Workshop on Ontology Matching (OM</source>
          <year>2023</year>
          )
          <article-title>co-located with</article-title>
          <source>ISWC</source>
          <year>2023</year>
          , volume
          <volume>3591</volume>
          ,
          <string-name>
            <surname>Athènes</surname>
          </string-name>
          , Greece,
          <year>2023</year>
          , pp.
          <fpage>191</fpage>
          -
          <lpage>199</lpage>
          . URL: https://hal.science/hal-04524356.
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>Y.</given-names>
            <surname>He</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Chen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Dong</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Horrocks</surname>
          </string-name>
          ,
          <article-title>Exploring large language models for ontology alignment</article-title>
          ,
          <year>2023</year>
          . URL: https://arxiv.org/abs/2309.07172. arXiv:
          <volume>2309</volume>
          .
          <fpage>07172</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>M.</given-names>
            <surname>Fleissner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L. C.</given-names>
            <surname>Vankadara</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Ghoshdastidar</surname>
          </string-name>
          ,
          <article-title>Explaining kernel clustering via decision trees</article-title>
          ,
          <year>2024</year>
          . URL: https://arxiv.org/abs/2402.09881. arXiv:
          <volume>2402</volume>
          .
          <fpage>09881</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>N.</given-names>
            <surname>Kokash</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Makhnist</surname>
          </string-name>
          ,
          <article-title>Using decision trees for interpretable supervised clustering</article-title>
          ,
          <source>SN Computer Science</source>
          <volume>5</volume>
          (
          <year>2024</year>
          )
          <article-title>268</article-title>
          . URL: https://doi.org/10.1007/s42979-023-02590-7. doi:
          <volume>10</volume>
          . 1007/s42979-023-02590-7.
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>