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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Detection of COVID-19-Related Conspiracy Theories in Tweets using Transformer-Based Models and Node Embedding Techniques</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Youri Peskine</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Paolo Papotti</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Raphaël Troncy</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>EURECOM</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>France</string-name>
        </contrib>
      </contrib-group>
      <abstract>
        <p>With the amount of information shared on the web increasing on a daily basis, we are prone to face more misinformation online. This is especially true on social media websites, where users have good amount of freedom to share their opinion. During the COVID-19 pandemic, numerous conspiracy theories were shared on Twitter. In this “FakeNews Detection” task, the goal is to detect COVID-19-related conspiracy theories using tweet text and user interaction graph. We tackled this challenge using Transformer-based models (CT-BERT) and node embedding techniques (node2vec) with classification objective models. Our best model obtains a MCC score of 0.719 on the test data.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        Transformer-based [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] models have achieved state-of-the-art performance for various NLP
tasks [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. These models are pre-trained on large corpus of text, and can be fine-tuned for a
specific task on a smaller corpus. An example is COVID-Twitter-BERT (CT-BERT) [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], which is
a pre-trained model on large corpus of Twitter data on the topic of COVID-19. This makes it
suited for tasks 1 and 3 of this challenge. This year’s task 1 is very similar to last year’s task
3 [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], in which we participated [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. In our previous experience, the CT-BERT model was the
most performing one.
      </p>
      <p>
        The second task requires methods that leverage graph data. Indeed, the provided data is
composed of a graph of interaction between Twitter users, as well as some information about
the user itself. More information about the data can be found in the task description paper
[
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This task of node classification can be tackled using node embedding techniques from
sequence-based models (e.g. node2vec) or GNNs (e.g. GCN) [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Sequence-based models learn
the embeddings of a node by using the structure of the graph and the neighbors of a node,
without capturing any information about the node features. The node classification can then
be done with diferent models, from the learned node embedding, using traditional classifier
approaches such as Multi Layer Perceptron (MLP) or Random Forest (RF). The GNN-based
approach optimize both the embedding and the classification task at the same time. It utilizes
the structure of the graph, as well as the node features.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Approach</title>
      <p>In order to tackle this challenge, we studied text-classification transformer-models for tasks 1
and 3, and node-classification models for tasks 2 and 3. Our approach leverages multiple
CTBERT models for text-classification and node2vec in combination with simple classifiers (MLP,
RF) for node-classification. We also experimented with GNN without much success and we do
not report these results. In all experiments, we split the data into 5 stratified cross-validation
sets.</p>
      <sec id="sec-3-1">
        <title>3.1. Text Classification</title>
        <p>First, we used some basic pre-processing on the text data. We replaced all emojis with their
textual meaning using the emoji Python library.2 We also removed the hashtag (‘#’ character)
from the tweets. Next, we approached task 1 as a multi-label 3-way classification problem. We
trained 5 CT-BERT models, one for each cross-validation fold, using a custom loss function.
The last layer of our models has 27 dimensions, three for each of the 9 conspiracy theories
(discuss, support, not related). We build 9 diferent Cross-Entropy losses, each measuring the
performance of the model at detecting one conspiracy theory. These Cross-Entropy losses are
weighted independently, proportionally to the inverse of the frequency of the respective class
in the training data. Then, the final loss is the unweighted sum of the 9 diferent losses.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Node Classification</title>
        <p>We used a node2vec model to generate node embeddings, and then used standard
machinelearning classifiers to perform the node classification.</p>
        <p>
          We first build the graph from the user-interaction data, using the networkx Python
library [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ].3 This graph is composed of around 1.7 Million nodes (representing the Twitter users)
and 270 Million directed edges (representing the interaction between the users). We run the
node2vec algorithm on that graph, using nodevectors Python library. 4 We generate 10 random
walks per node, of length 40, with the return parameter set to p=1 and the in-out parameter set
to q=1/2. The dimension of the embeddings is 32.
2https://github.com/carpedm20/emoji/
3https://github.com/networkx/networkx
4https://github.com/VHRanger/nodevectors
        </p>
        <p>
          Next, we train some popular machine-learning classifier algorithms available on the
scikitlearn Python library [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ]5 to perform node classification. Those algorithms take as input the
32-dimension vector from the node2vec model and perform a binary-classification objective.
Random Forest (RF) classifier obtained the best results. We also trained a MLP classification
head as well.6
        </p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Tweet Classification Using Both Text and Graph Data</title>
        <p>We used both graph and textual data for the third task of the challenge. We trained a classifier
from the concatenation of both text and graph features, without any form of feature space
normalization. Those graph features are the 32-dimension vector from the node embeddings,
and the textual features are the 27-dimension vector output of the task 1 model. The training
loss is similar to the one described in Section 3.1.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Results and Analysis</title>
      <p>In this section, we first describe each run, and then analyse the main takeaways from the results.
We present our results for this challenge in Table 1.</p>
      <sec id="sec-4-1">
        <title>4.1. Runs description</title>
        <p>For the first task, we performed an ensembling of the 5 models trained on each fold of the cross
validation split (run 001). This ensembling was done with majority voting. In case of a draw
between two classes, 1 would have priority over 2 and 3, and 3 over 2. This order follows the
proportion of samples we have in the data. Run 002 is the single best model of the 5 models.
Run 003 is the same ensembling as run 001 but with the ’cannot determine’ labeling if there is
less than 4 models out of 5 in agreement. The ensembling (run 001) obtained the best results.</p>
        <p>The second task was more challenging and results are lower compared to task 1. We propose
multiple ensembling methods from the models trained on each fold of the cross-validation split.
5List of tested classifiers: KNeighborsClassifier, GaussianProcessClassifier, DecisionTreeClassifier,
RandomForestClassifier, AdaBoostClassifier, GaussianNB, QuadraticDiscriminantAnalysis and GradientBoostingClassifier
6The hyper-parameters for the MLP model are: layers of 32-16-8-1, dropout p=0.1, ReLU activation function
We trained 5 MLP models and 5 RF models. Run 101, 103, and 105 are ensembling of those
models. Run 106 is the same as run 101 with the ’cannot determine’ labeling logic as in run
003. Run 102 is the best single MLP model from run 101. This run obtained the best results,
out-performing the ensembling (run 101). We also submitted our run 101 as a sixth run (106)
because we did not use any pre-trained model.</p>
        <p>For the last task, we first propose the same models as the first task, without using the graph
data. Runs 201, 202 and 203 are the same as runs 001, 002 and 003. Results are slightly diferent
because the test data is diferent from task 1 and 3. Then, we also propose models using both
text and graph data, using the approach described in Section 3.3. Run 204 is an ensembling
of the MLP models trained on each fold of the cross validation split and run 205 is the single
best MLP model. The best performing model for this third task is the ensembling of CT-BERT
models, only on text data (same as run 001).</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Main takeaways</title>
        <p>
          A first takeaway from these results is that the CT-BERT model is suited for text classification
tasks and obtains very good results, even if slightly lower than in 2021 [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]. The ensembling
of models trained on diferent cross-validation fold improves the results with textual models
(run 001, 201 and 204), but not for the graph-based approach (run 101, 103 and 105). Also, the
‘cannot determine’ labeling did not improve the results over the normal majority voting (runs
003, 104 and 203). The overall approach for task 2 gives lower results than task 1, but the task
is also more challenging. The MLP classifier from the node embeddings is a baseline that can
definitely be improved. For example, we could try to reduce the size of the very large graph by
removing some nodes in order to remove noise. For the last task, the MLP fusion model, taking
both text-based features and graph-based features (run 204), did not improve on the text-only
CT-BERT model (run 201). The fusion model could still be improved to correctly use both kinds
of data and improve the overall results.
        </p>
        <p>Comparing these results with last year challenge, we did not see a major improvement in the
overall score, even though we had access to more data this year. Regarding the results for each
conspiracy theory, the best results are obtained for the ‘Harmful Radiation/Influence’ (0.830),
‘New World Order’ (0.830), and ‘Population reduction’ (0.876) conspiracies. The worst result is
obtained for the conspiracy theory ‘Antivax’ (0.563). More data does not seem to correlate to
better results for each conspiracy as well, since ‘Antivax’ has almost four times more data than
‘Harmful Radiation/influence’ and still perform significantly worse. This is partially due to the
weighting of the loss function, which emphasizes the classes with a smaller number of samples.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>In this paper, we propose a transformer-based method to detect COVID-19-related conspiracy
theories in tweets, composed of an ensembling of CT-BERT models. We also propose a node
embedding-based techniques to detect misinformation spreader in the user-interaction graph,
using node2vec and an MLP classification head. Our best model obtains a MCC score of 0.719
on the test data.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgements</title>
      <p>This work has been partially supported by CHIST-ERA within the CIMPLE project
(CHIST-ERA19-XAI-003).</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>K.</given-names>
            <surname>Pogorelov</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. T.</given-names>
            <surname>Schroeder</surname>
          </string-name>
          , S. Brenner, ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Maulana</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Langguth</surname>
          </string-name>
          ,
          <article-title>Combining Tweets and Connections Graph for FakeNews Detection at MediaEval 2022</article-title>
          , in: Multimedia Benchmark Workshop,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>S.</given-names>
            <surname>Minaee</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Kalchbrenner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Cambria</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Nikzad</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Chenaghlu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Gao</surname>
          </string-name>
          ,
          <article-title>Deep Learning-Based Text Classification: A Comprehensive Review</article-title>
          ,
          <source>ACM Computer Survey</source>
          <volume>54</volume>
          (
          <year>2021</year>
          ). URL: https: //doi.org/10.1145/3439726.
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>J.</given-names>
            <surname>Devlin</surname>
          </string-name>
          , M.-
          <string-name>
            <given-names>W.</given-names>
            <surname>Chang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Toutanova</surname>
          </string-name>
          , BERT:
          <article-title>Pre-training of Deep Bidirectional Transformers for Language Understanding, in: Conference of the North American Chapter of the Association for Computational Linguistics (ACL), Association for Computational Linguistics</article-title>
          , Minneapolis, Minnesota,
          <year>2019</year>
          , pp.
          <fpage>4171</fpage>
          -
          <lpage>4186</lpage>
          . URL: https://aclanthology.org/N19-1423.
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>T. N.</given-names>
            <surname>Kipf</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Welling</surname>
          </string-name>
          ,
          <article-title>Semi-Supervised Classification with Graph Convolutional Networks</article-title>
          ,
          <source>in: International Conference on Learning Representations (ICLR)</source>
          ,
          <year>2017</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>A.</given-names>
            <surname>Grover</surname>
          </string-name>
          ,
          <string-name>
            <surname>J. Leskovec,</surname>
          </string-name>
          <article-title>Node2vec: Scalable feature learning for networks</article-title>
          ,
          <source>in: 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Association for Computing Machinery</source>
          ,
          <year>2016</year>
          , pp.
          <fpage>855</fpage>
          --
          <lpage>864</lpage>
          . URL: https://doi.org/10.1145/2939672.2939754.
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>A.</given-names>
            <surname>Vaswani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Shazeer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Parmar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Uszkoreit</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Jones</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. N.</given-names>
            <surname>Gomez</surname>
          </string-name>
          , L. u. Kaiser,
          <string-name>
            <surname>I. Polosukhin</surname>
          </string-name>
          , Attention is All you Need,
          <source>in: Advances in Neural Information Processing Systems (NeurIPS)</source>
          , Curran Associates, Inc.,
          <year>2017</year>
          . URL: https://proceedings.neurips.cc/paper/2017/file/ 3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>T.</given-names>
            <surname>Wolf</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Debut</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Sanh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Chaumond</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Delangue</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Moi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Cistac</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Rault</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Louf</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Funtowicz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Davison</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Shleifer</surname>
          </string-name>
          , P. von Platen, C. Ma,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Jernite</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Plu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Xu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T. Le</given-names>
            <surname>Scao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Gugger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Drame</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Q.</given-names>
            <surname>Lhoest</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Rush</surname>
          </string-name>
          , Transformers:
          <article-title>State-of-the-art natural language processing</article-title>
          ,
          <source>in: Conference on Empirical Methods in Natural Language Processing (EMNLP)</source>
          ,
          <source>System Demonstrations, Association for Computational Linguistics</source>
          ,
          <year>2020</year>
          , pp.
          <fpage>38</fpage>
          -
          <lpage>45</lpage>
          . URL: https: //aclanthology.org/
          <year>2020</year>
          .emnlp-demos.6. doi:
          <volume>10</volume>
          .18653/v1/
          <year>2020</year>
          .emnlp-demos.
          <volume>6</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>M.</given-names>
            <surname>Müller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Salathé</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P. E.</given-names>
            <surname>Kummervold</surname>
          </string-name>
          ,
          <string-name>
            <surname>COVID-Twitter-BERT: A Natural Language Processing Model to Analyse</surname>
          </string-name>
          COVID-19
          <source>Content on Twitter</source>
          ,
          <year>2020</year>
          . arXiv:
          <year>2005</year>
          .07503.
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>K.</given-names>
            <surname>Pogorelov</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. T.</given-names>
            <surname>Schroeder</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Brenner</surname>
          </string-name>
          , J. Langguth,
          <source>FakeNews: Corona Virus and Conspiracies Multimedia Analysis Task at MediaEval</source>
          <year>2021</year>
          , in: Multimedia Benchmark Workshop,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Peskine</surname>
          </string-name>
          , G. Alfarano,
          <string-name>
            <surname>I. Harrando</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Papotti</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Troncy</surname>
          </string-name>
          ,
          <string-name>
            <surname>Detecting</surname>
            <given-names>COVID</given-names>
          </string-name>
          -19
          <article-title>-related conspiracy theories in tweets</article-title>
          , in: CEUR (Ed.),
          <source>MediaEval Benchmarking Initiative for Multimedia Evaluation Workshop</source>
          ,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>M.</given-names>
            <surname>Ilya</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Dmitrii</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Nikita</surname>
          </string-name>
          ,
          <string-name>
            <surname>S. Lovro,</surname>
          </string-name>
          <article-title>Survey on graph embeddings and their applications to machine learning problems on graphs</article-title>
          ,
          <source>PeerJ Computer Science</source>
          (
          <year>2021</year>
          ). URL: https://doi.org/10. 7717/peerj-cs.
          <volume>357</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>A. A.</given-names>
            <surname>Hagberg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. A.</given-names>
            <surname>Schult</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P. J.</given-names>
            <surname>Swart</surname>
          </string-name>
          ,
          <article-title>Exploring network structure, dynamics, and function using networkx</article-title>
          ,
          <source>in: 7th Python in Science Conference</source>
          , Pasadena, CA USA,
          <year>2008</year>
          , pp.
          <fpage>11</fpage>
          -
          <lpage>15</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>F.</given-names>
            <surname>Pedregosa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Varoquaux</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Gramfort</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Michel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Thirion</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Grisel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Blondel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Prettenhofer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Weiss</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Dubourg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Vanderplas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Passos</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Cournapeau</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Brucher</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Perrot</surname>
          </string-name>
          , E. Duchesnay,
          <article-title>Scikit-learn: Machine learning in Python</article-title>
          ,
          <source>Journal of Machine Learning Research</source>
          <volume>12</volume>
          (
          <year>2011</year>
          )
          <fpage>2825</fpage>
          -
          <lpage>2830</lpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>