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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>An Approach to Correction of Erroneous Links in Knowledge Graphs</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>André Melo</string-name>
          <email>andre@informatik.uni-mannheim.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Heiko Paulheim</string-name>
          <email>heiko@informatik.uni-mannheim.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Mannheim</institution>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2017</year>
      </pub-date>
      <abstract>
        <p>Enriching and cleaning datasets are tasks relevant to most largescale knowledge graphs, which are known to be noisy and incomplete. In this paper, we propose one approach to fix wrong facts which originate from confusion between entities. This is a common source of errors in Wikipedia, from which DBpedia and YAGO are extracted, and in open information extraction systems, e.g. NELL. Our approach generates candidate subjects and objects to fix triples by exploiting disambiguation links and approximate string matching. We run our approach on DBpedia and NELL and perform a manual evaluation of the generated corrections.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>CCS CONCEPTS</title>
      <p>• Information systems → Data cleaning; • Computing
methodologies → Semantic networks; Statistical relational
learning; Machine learning;</p>
    </sec>
    <sec id="sec-2">
      <title>INTRODUCTION</title>
      <p>Knowledge graphs are known to be both often incomplete and
incorrect. Several link prediction and error detection methods have
been proposed, however, few of them explicitly focus on error
correction or address the problem of choosing which absent facts
should be added to the knowledge graph.</p>
      <p>The problem is that the number of possible relation assertions
grows quadratically with the number of instances nc = ni2nr − nf ,
where ni is the number of instances, nr the number of relations
and nf the number of existing facts in the graph. For large datasets
such as DBpedia, Wikidata and YAGO, computing the confidence
score of all these facts is challenging. While pruning possible facts
which violate ontology constraints, especially domain and range
restrictions of relations, can significantly reduce the search space,
the problem is still very challenging. To illustrate the size of the
search space, in DBpedia (2016-10) nc ≈ 4.4 × 1017 facts; when
ifltering those triples which violate the domain and range restriction
the number is reduced to nc ≈ 2.8 × 1017, which is still too large to
compute confidence for all those candidates.</p>
      <p>A promising approach for enriching a KG with some of its
missing facts is the correction of erroneous facts. Some of the wrong
facts which exist in a KG can be corrected. The error originates
from some problem in the knowledge acquisition process, or in the
source data. A good example of the latter are errors in Wikipedia,
which serves as the main source of DBpedia and YAGO. If any
of the links in the infobox are wrong, the extraction process
generates a wrong fact. NELL, on the other hand, has text as main
source of information and in many cases the source text has correct
information, which cannot be extracted correctly.</p>
      <p>In both cases it is common that an instance is confused with
another one of a similar name (i.e., label or IRI). For example, the fact
formerTeam( Alan_Ricard, Buffalo_Bill) is an erroneous fact
from DBpedia which originates from a typo in Wikipedia: when
referring to the NFL team Buffalo_Bills, the s was missing,
therefore, the NFL team was confused with the character Buffalo_Bill.
In NELL the entity insect_raccoon exists because of problems
when extracting the fact that raccoons prey on insects, and is
confused with mammal_raccoon.</p>
      <p>
        Some relation assertion error detection approaches, such as
PaTyBRED [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] and SDValidate [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], rely on type information, and since
erroneous type assertions are also a common problem, that might
result in correct relation assertions with an instance of incorrect or
incomplete types being wrongly identified as erroneous. Therefore,
combining such methods with type prediction [
        <xref ref-type="bibr" rid="ref12 ref6">6, 12</xref>
        ] is beneficial
to rule out cases where the error is detected rather due to a missing
or incorrect type of the subject or object than due to an erroneous
relation assertion.
      </p>
      <p>Therefore, it is relevant to make a careful analysis of detected
errors, identify the source of each error, and if possible correct
them. In this paper, we propose CoCKG (Correction of Confusions
in Knowledge Graphs), an automatic correction approach which
resolves relation assertion errors caused by instance confusion.
The approach relies on error detection methods as well as type
predictors to asses the confidence of the corrected facts. It uses
approximate string matching and exploits both searching for
entities with similar IRIs as well as Wikipedia disambiguation pages (if
available) to find candidate instances for correcting the facts.
2</p>
    </sec>
    <sec id="sec-3">
      <title>RELATED WORK</title>
      <p>In the knowledge graph context, there are mainly error detection
and link prediction approaches. Both are closely related to our
problem: while error detection deletes wrong triples, link prediction
aims at adding new triples. In both cases, the approaches learn a KG
model which is capable of assigning confidence values to triples.</p>
      <p>
        KG embedding models [
        <xref ref-type="bibr" rid="ref1 ref10 ref14">1, 10, 14</xref>
        ] are currently the best
performing approaches in the link prediction task. Other models rely on
directly observed features, e.g., the path ranking algorithm (PRA)
[
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. A more detailed description of link prediction methods can be
found in [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. It is important to note that none of the link
prediction approaches mentioned address the problem of covering the
candidate triples space (of size nc as discussed in the introduction).
Our approach, on the other hand, exploits the assumption that
erroneous facts often have a corresponding correct fact in order to
reduce that space. Error detection approaches, such as SDValidate
and PaTyBRED, focus on the detecting of already existing erroneous
triples. It has been shown that state-of-the-art embeddings perform
worse than PaTyBRED in the error detection task [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. A survey
covering various KG refinement methods can be found in [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ].
      </p>
      <p>
        Rule-based systems, such as AMIE [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], cannot assign scores to
arbitrary triples. However, they could be used to restrict the nc
search space by identifying high confidence soft rules and using
the missing facts from instances where the rule does not hold as
candidates. Combining them with previously mentioned KG models
would be an interesting line of reasearch, however, it is out of the
scope of this paper.
      </p>
      <p>
        Wang et al. [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] studied the problem of erroneous links in Wikipedia,
which is also the source of many errors of DBpedia. They model
the Wikipedia links as a weighted directed mono-relational graph,
and propose the LinkRank algorithm which similar to PageRank,
but instead of ranking the nodes (entities), it ranks the links. They
use LinkRank to generate candidates for the link correction and
use textual features from the description of articles to learn a SVM
classifier that can detect errors and choose the best candidate for
correction. While this is a closely related problem, which can help
mitigate the problem studied in this paper, their method cannot
be directly applied on arbitrary knowledge graphs. Our approach
takes advantage of the multi-relational nature of KGs, entity types,
ontological information and the graph structure.
      </p>
    </sec>
    <sec id="sec-4">
      <title>3 PROPOSED APPROACH</title>
      <p>Our approach consists of first running an error detection algorithm
(PaTyBRED in the case of this paper), selecting the top-k facts
most likely to be wrong. In the next step, the error is heuristically
verified to be an actual relation assertion error and not caused
by missing type assertions in the object or subject with a type
predictor tp. In the final step, candidate entities are retrieved, and
if any of the candidates significantly improves the likelihood of
the triple being right, we replace it by that candidate. The function
correct_triple in Algorithm 1 gives an overview of how CoCKG
works. The parameter K is the set of all triples in the knowledge
graph, Ter r is the set of triple and confidence pairs generated by
the error detection model (ed), tp is the type predictor, mc is the
minimum confidence threshold, and mcд the minimum confidence
gain threshold, i.e. the ratio of the new and old triple scores. In the
next subsections we discuss the other parts in more details.</p>
    </sec>
    <sec id="sec-5">
      <title>3.1 Type Prediction</title>
      <p>
        After selecting the k triples most likely to be wrong, we first check
if their confidence is low because of missing or wrong instance
types (subject or object). In order to do that, we run a type predictor
tp on the subject and object instances. In this paper, we use as tp
a multilabel random forest classifier based on qualified links (i.e.
ingoing links paired with subject type and outgoing links paired
with object type), as described in [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. If the set of predicted types of
the subject are diferent from the actual types, we change the type
features used by ed and compute a new confidence for the triple (c.f.
conf_nt). If the new score satisfies mc and mcд, then we conclude
that the error was in the subject type assertions. The same is done
for the object, and if in neither case the confidence thresholds are
Algorithm 1 Knowledge base correction process
1: function correct_triples(K , Ter r , ed, tp, mc, mcд)
2: Tcor r ← ∅
3: for t, scor et ∈ Ter r do
4: s, p, o ← t
5: stp ← predict_types(tp, s)
6: otp ← predict_types(tp, o)
7: if ¬(conf_nt(ed, t, s, stp ) ∨ conf_nt(ed, t, o, otp )) then
8: scand ← get_candidates(s)
9: ocand ← get_candidates(o)
10: Tcand ← {(si, p, o) |si ∈ scand } ∪ {(s, p, oi ) |oi ∈ ocand }
11: Tcand ← Tcand − K
12: cbest , maxconf ← nil, conf
13: for c ∈ Tcand do
14: if s ∈ domain(p) ∧ o ∈ r anдe (p) then
15: scor ec ← conf(ed, c)
16: if scor ec ≥ mc ∧ scor ec /scor et ≥ mcд then
17: cbest , maxconf ← c, scor ec
18: end if
19: end if
20: end for
21: if cbest , nil then
22: Tcor r ← Tcor r ∪ {(cbest , t ) }
23: end if
24: end if
25: end for
26: return Tcor r
27: end function
satisfied, we proceed to the next part where we try to substitute
the subject and object with their respective lists of candidates.
      </p>
      <p>Combining the type prediction process with the error detection
also has the advantage that the newly predicted types can be
validated on triples containing the instance whose types were predicted.
This can help support, or contradict the type predictor, possibly
detecting types which are wrongly predicted by identifying triples
where the score is lowered with the new types.</p>
    </sec>
    <sec id="sec-6">
      <title>3.2 Retrieving Candidates</title>
      <p>One simple way to find candidate entities to resolve entity
confusions is to use the disambiguation links. Since disambiguation pages
are only available for Wikipedia-based knowledge graphs, and
furthermore are not available for each entity (e.g. Ronaldo has no
disambiguation page), and in some cases the disambiguation pages
miss important entities (e.g. the page Bluebird_(disambiguation)
misses the entity Bluebird_(horse), hence, we cannot correct the
fact grandisre(Miss_Potential,Bluebird)), we require an
additional source of candidates.</p>
      <p>Since in our experiments we consider DBpedia and NELL, which
have informative IRIs (in the case of DBpedia extracted from the
correspondent Wikipedia’s page), we search for candidate entities
which have similar IRIs. Alternatively, it could also be done with
entity labels. This would be useful in KGs which have uninformative
IRIs (e.g. Wikidata and Freebase). For simplicity, in this paper, we
refer to the informative part of an IRI as the “name” of the entity.</p>
      <p>
        Retrieving all the instances of similar names can be a complicated
task. This kind of problem is known as approximate string matching,
and it has been widely researched [
        <xref ref-type="bibr" rid="ref16 ref8">8, 16</xref>
        ]. For our method we use
an approximate string matching approach based on [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. First, we
remove the IRI’s prefix and work with the sufix as the entity’s name.
We then tokenize the names and construct a deletions dictionary
with all tokens being added with all possible deletions up to a
An Approach to Correction of Erroneous Links in Knowledge Graphs
maximum edit distance dmax threshold. This dictionary contains
strings as keys and lists with all tokens which can turn into the key
string with up to dmax deletions as values. Only pairs of tokens
which share a common deletion string can have an edit distance
less or equal than dmax . We also have a tokens dictionary which
has tokens as keys and lists of entities which contain a given token
as values. With that, given a token and a dmax we can easily obtain
all the entities which contain that a string approximately similar to
that token up to the maximum edit distance.
      </p>
      <p>When searching for entities similar to a given entity, we perform
queries for every token of the entity’s name and we require that
all tokens are matched. That is, for a certain entity to be
considered similar, it has to contain tokens similar to all the tokens of
the queried entity. A retrieved entity may have more tokens than
the queried entity, but not less. The idea is that in general, when
entering an entities name manually (e.g., in Wikipedia), it is
common to underspecify the entity, but highly unlikely to overspecify
it. E.g., it is more likely that Ronaldo is wrongly used instead of
Cristiano_Ronaldo than the other way around. Furthermore, it
reduces the number of matched entities.</p>
      <p>We also perform especial treatment on DBpedia and NELL entity
names because of peculiarities in their IRI structures. In DBpedia
it is common to have between parentheses information to help
disambiguate entities, which we consider unnecessary since the
entity types are used in the error detection method. In NELL the
ifrst token is always the type of the entity, therefore, for similar
reasons, we ignore it.
3.3</p>
    </sec>
    <sec id="sec-7">
      <title>Correcting Wrong facts</title>
      <p>At this point, for each assertion identified as erroneous, we have
our list of candidate instances for subject and object from the
disambiguation links and approximate string matching. We then compute
a custom similarity measure s (e1, e2) between an entity e1 and a
candidate e2. Each entity ei consists of a set of its tokens. The
measure we propose consists of two components. The first is the sum
of Levenshtein (dL ) distance of all matched tokens, and the second
considers the number of unmatched tokens to capture a diference
in specificity. The set of approximately matched token pairs is
represented by µ (e1, e2) and the constant c is the weight of the second
component. This measure is used to sort the retrieved candidates,
to prune them in case there are too many, and to break ties when
deciding which of the top-scoring candidates should be chosen.
s (e1, e2) =</p>
      <p>dL (t1, t2) + c</p>
      <p>X
(t1,t2) ∈µ (e1,e2)
|e1 | − |µ (e1, e2) |
|e1|
(1)</p>
      <p>In case the relation has domain or range restrictions, we remove
the candidates which violate these restrictions. Later, for each of
the candidates, we generate triples by substituting the subject and
object by each of the instances in its candidates lists (first substitute
subject only, then object only). That is, the total number of candidate
triples is the sum of the size of the subject and object candidates list.
We do not create candidate triples by substituting both the subject
and object at the same time because, although possible, we assume
58
21</p>
      <p>13
8</p>
      <p>WC
WW
CW
CC
64
14</p>
      <p>8
12
the simultaneous confusion of both instances to be highly unlikely.1
This is also done in order to make the number of candidate triples
linear instead of quadratic.</p>
      <p>We then remove the candidate triples which are already existent
in the KG. We compute the confidence of all candidate triples and
select that with highest confidence, given that mc and mcд are
satisfied. Our method then outputs a list of triple pairs containing
the wrong triple detected and the corrected triple predicted.
4</p>
    </sec>
    <sec id="sec-8">
      <title>EXPERIMENTS</title>
      <p>In our experiments we run CoCKG on DBpedia (2016-10) and NELL
(08m-690), then we manually evaluate the triples corrected by our
approach. We run PaTyBRED on both datasets and select top-1%
facts most likely to be errors to be processed by our correction
method. We classify each corrected fact in four diferent categories:
(1) WC: wrong fact turned into correct
(2) WW: wrong fact turned into another wrong fact
(3) CW: correct fact turned into wrong fact
(4) CC: correct fact turned into another correct fact</p>
      <p>Our approach was run with mc = 0.75, mcд = 2 and entity
similarity measure with c = 1.52. That resulted in 24,973 corrections
on DBpedia and 616 correction on NELL. It also detected that 873
(569) errors were caused by wrong types in DBpedia (NELL). Since
manually evaluating all these corrections would be impossible, we
randomly select 100 correction on each to perform the evaluation.</p>
      <p>The results of our manual evaluation are shown in Figure 1.
The proportion of facts successfully corrected (case 1) was rather
low. While our approach can potentially improve the results by
tweaking the parameters, and possibly using ensembles of diferent
type predictors and error detectors, it currently cannot be used as
a fully automatic approach. However, we believe that combining
our approach with active learning is a promising direction which,
with the help of specialists, could significantly improve results.</p>
      <p>When evaluating some relations individually, we notice that
some of them achieve good results. E.g., the relations sire, damsire,
grandsire and subsequentWork reaching more than 90% of
successful corrections (case 1). The results are good for these relations
because horses are often named after other entities and artists often
have albums named after themselves, which makes confusions easy
to happen.
1For that to happen in the case of DBpedia, a Wikipedia user would have to go to the
wrong article page and insert a wrong link in the infobox.
2The parameter values were selected based on heuristics and may not be optimal</p>
      <p>
        One of the problems of our approach is that since it relies on
PaTyBRED, which cannot find many relevant path features on
DBpedia and NELL [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], it is dificult to distinguish between
candidate entities of same type. For example, in NELL, the entity
person_paul as object of book_writer relation is always corrected
with writer_paul_feval.
      </p>
      <p>The decision to generate candidate triples by corrupting
either the subject or object seemed to have worked well for
DBpedia, where we could not find a triple where both subject and
object were wrong. On the other hand, in NELL such case was
observed a few times, e.g. ismultipleof(musicinstrument_herd ,
musicinstrument_buffalo) whose object was corrected to
mammal_buffalo but the subject remained wrong.</p>
      <p>Also, our assumption that confusions tend to use a more general
IRI instead of a more specific, requiring all tokens of the queried to
be matched, does not always hold. One example in DBpedia which
contradicts this assumption is language(Paadatha_Thenikkal ,
Tamil_cinema), whose corrected object would be Tamil_language
and could not be retrieved by our approach. While this can be a
problem, dropping this assumption also means that more
candidates entities will be retrieved, increasing the number of unrelated
candidates, resulting in more candidate triples which need to be
tested and possibly more occurrences of cases 2 and 3. Further
experiments would have to be conducted in order to evaluate the
efects of such change.
5</p>
    </sec>
    <sec id="sec-9">
      <title>CONCLUSION</title>
      <p>In this paper we proposed CoCKG, an approach for correcting
erroneous facts originated from entity confusions. The experiments
show that CoCKG is capable of correcting wrong triples with
confused instances, with estimated precision of 21% of the produced
corrections in DBpedia and 14% in NELL. The low precision
values obtained do not allow this process, as of now, to be used for
fully automatic KG enrichment. Nevertheless, it works as a proof
of concept and can be useful, e.g., as suggestions from which a user
would ultimately decide whether to execute.</p>
      <p>In the future it would be interesting to adapt this method to
support active learning. Since guaranteeing the quality of the newly
generated facts is crucial, having input from the user to clarify
borderline cases and improve the overall results would be highly
valuable. Furthermore, using an ensemble of diferent KG models
with diferent characteristics, e.g. KG embeddings, instead of a
single model may potentially increase the robustness of the system.
Finally, it would be worth adding textual features from entities
descriptions to help determine if a pair of entities is related or not.</p>
    </sec>
    <sec id="sec-10">
      <title>ACKNOWLEDGMENTS</title>
      <p>The work presented in this paper has been partly supported by the
Ministry of Science, Research and the Arts Baden-Württemberg in
the project SyKo2W2 (Synthesis of Completion and Correction of
Knowledge Graphs on the Web).</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>Antoine</given-names>
            <surname>Bordes</surname>
          </string-name>
          , Nicolas Usunier, Alberto Garcia-Duran,
          <string-name>
            <given-names>Jason</given-names>
            <surname>Weston</surname>
          </string-name>
          , and Oksana Yakhnenko. [n. d.].
          <article-title>Translating Embeddings for Modeling Multi-relational Data</article-title>
          .
          <source>In Advances in Neural Information Processing Systems</source>
          <volume>26</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>Luis</given-names>
            <surname>Antonio</surname>
          </string-name>
          <string-name>
            <given-names>Galárraga</given-names>
            , Christina Teflioudi, Katja Hose, and
            <surname>Fabian</surname>
          </string-name>
          <string-name>
            <given-names>M.</given-names>
            <surname>Suchanek</surname>
          </string-name>
          .
          <year>2013</year>
          .
          <article-title>AMIE: association rule mining under incomplete evidence in ontological knowledge bases</article-title>
          .
          <source>In 22nd International World Wide Web Conference, WWW '13</source>
          , Rio de Janeiro, Brazil, May
          <volume>13</volume>
          -17,
          <year>2013</year>
          ,
          <string-name>
            <given-names>Daniel</given-names>
            <surname>Schwabe</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Virgílio A. F.</given-names>
            <surname>Almeida</surname>
          </string-name>
          , Hartmut Glaser, Ricardo A.
          <string-name>
            <surname>Baeza-Yates</surname>
          </string-name>
          , and Sue B. Moon (Eds.).
          <source>International World Wide Web Conferences Steering Committee / ACM</source>
          ,
          <fpage>413</fpage>
          -
          <lpage>422</lpage>
          . http://dl. acm.org/citation.cfm?id=
          <fpage>2488425</fpage>
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>Ni</given-names>
            <surname>Lao</surname>
          </string-name>
          and
          <string-name>
            <given-names>William W.</given-names>
            <surname>Cohen</surname>
          </string-name>
          .
          <year>2010</year>
          .
          <article-title>Relational Retrieval Using a Combination of Path-constrained Random Walks</article-title>
          .
          <source>Mach. Learn</source>
          .
          <volume>81</volume>
          ,
          <issue>1</issue>
          (Oct.
          <year>2010</year>
          ),
          <fpage>53</fpage>
          -
          <lpage>67</lpage>
          . https: //doi.org/10.1007/s10994-010-5205-8
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>Andre</given-names>
            <surname>Melo</surname>
          </string-name>
          and
          <string-name>
            <given-names>Heiko</given-names>
            <surname>Paulheim</surname>
          </string-name>
          .
          <year>2017</year>
          .
          <article-title>Detection of Relation Assertion Errors in Knowledge Graphs</article-title>
          .
          <source>In Proceedings of the 9th International Conference on Knowledge Capture, K-CAP</source>
          <year>2017</year>
          , Austin, TX, USA, December 4-
          <issue>6</issue>
          ,
          <year>2017</year>
          . ACM.
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>André</given-names>
            <surname>Melo</surname>
          </string-name>
          and
          <string-name>
            <given-names>Heiko</given-names>
            <surname>Paulheim</surname>
          </string-name>
          .
          <year>2017</year>
          .
          <article-title>Local and global feature selection for multilabel classification with binary relevance</article-title>
          .
          <source>Artificial Intelligence Review</source>
          (
          <year>2017</year>
          ),
          <fpage>1</fpage>
          -
          <lpage>28</lpage>
          . https://doi.org/10.1007/s10462-017-9556-4
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>André</given-names>
            <surname>Melo</surname>
          </string-name>
          , Heiko Paulheim, and
          <string-name>
            <given-names>Johanna</given-names>
            <surname>Völker</surname>
          </string-name>
          .
          <year>2016</year>
          .
          <article-title>Type Prediction in RDF Knowledge Bases Using Hierarchical Multilabel Classification</article-title>
          .
          <source>In Proceedings of the 6th International Conference on Web Intelligence, Mining and Semantics (WIMS '16)</source>
          . ACM, New York, NY, USA, Article
          <volume>14</volume>
          , 10 pages. https://doi.org/10.1145/ 2912845.2912861
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>Stoyan</given-names>
            <surname>Mihov</surname>
          </string-name>
          and Klaus U. Schulz.
          <year>2004</year>
          .
          <article-title>Fast Approximate Search in Large Dictionaries</article-title>
          .
          <source>Comput. Linguist</source>
          .
          <volume>30</volume>
          ,
          <issue>4</issue>
          (Dec.
          <year>2004</year>
          ),
          <fpage>451</fpage>
          -
          <lpage>477</lpage>
          . https://doi.org/10. 1162/0891201042544938
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>Gonzalo</given-names>
            <surname>Navarro</surname>
          </string-name>
          .
          <year>2001</year>
          .
          <article-title>A Guided Tour to Approximate String Matching</article-title>
          .
          <source>ACM Comput. Surv</source>
          .
          <volume>33</volume>
          ,
          <issue>1</issue>
          (March
          <year>2001</year>
          ),
          <fpage>31</fpage>
          -
          <lpage>88</lpage>
          . https://doi.org/10.1145/375360.375365
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>Maximilian</given-names>
            <surname>Nickel</surname>
          </string-name>
          , Kevin Murphy, Volker Tresp, and
          <string-name>
            <given-names>Evgeniy</given-names>
            <surname>Gabrilovich</surname>
          </string-name>
          .
          <year>2016</year>
          .
          <article-title>A Review of Relational Machine Learning for Knowledge Graphs</article-title>
          .
          <source>Proc. IEEE 104</source>
          ,
          <issue>1</issue>
          (
          <year>2016</year>
          ),
          <fpage>11</fpage>
          -
          <lpage>33</lpage>
          . https://doi.org/10.1109/JPROC.
          <year>2015</year>
          .2483592
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <surname>Maximilian</surname>
            <given-names>Nickel</given-names>
          </string-name>
          , Volker Tresp, and Hans peter Kriegel.
          <year>2011</year>
          .
          <article-title>A Three-Way Model for Collective Learning on Multi-Relational Data</article-title>
          .
          <source>In Proceedings of the 28th International Conference on Machine Learning (ICML-11)</source>
          . ACM. http://www. icml-2011.org/papers/438_icmlpaper.pdf
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>Heiko</given-names>
            <surname>Paulheim</surname>
          </string-name>
          .
          <year>2017</year>
          .
          <article-title>Knowledge graph refinement: A survey of approaches and evaluation methods</article-title>
          .
          <source>Semantic Web</source>
          <volume>8</volume>
          ,
          <issue>3</issue>
          (
          <year>2017</year>
          ),
          <fpage>489</fpage>
          -
          <lpage>508</lpage>
          . https://doi.org/10. 3233/SW-160218
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>Heiko</given-names>
            <surname>Paulheim</surname>
          </string-name>
          and
          <string-name>
            <given-names>Christian</given-names>
            <surname>Bizer</surname>
          </string-name>
          .
          <year>2013</year>
          .
          <article-title>Type Inference on Noisy RDF Data</article-title>
          . Springer Berlin Heidelberg, Berlin, Heidelberg,
          <fpage>510</fpage>
          -
          <lpage>525</lpage>
          . https://doi.org/10.1007/ 978-3-
          <fpage>642</fpage>
          -41335-3_
          <fpage>32</fpage>
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>Heiko</given-names>
            <surname>Paulheim</surname>
          </string-name>
          and
          <string-name>
            <given-names>Christian</given-names>
            <surname>Bizer</surname>
          </string-name>
          .
          <year>2014</year>
          .
          <article-title>Improving the Quality of Linked Data Using Statistical Distributions</article-title>
          .
          <source>Int. J. Semant. Web Inf. Syst</source>
          .
          <volume>10</volume>
          ,
          <issue>2</issue>
          (April
          <year>2014</year>
          ),
          <fpage>63</fpage>
          -
          <lpage>86</lpage>
          . https://doi.org/10.4018/ijswis.2014040104
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <surname>Théo</surname>
            <given-names>Trouillon</given-names>
          </string-name>
          , Johannes Welbl,
          <string-name>
            <given-names>Sebastian</given-names>
            <surname>Riedel</surname>
          </string-name>
          , Éric Gaussier, and
          <string-name>
            <given-names>Guillaume</given-names>
            <surname>Bouchard</surname>
          </string-name>
          .
          <year>2016</year>
          .
          <article-title>Complex Embeddings for Simple Link Prediction</article-title>
          .
          <source>CoRR abs/1606</source>
          .06357 (
          <year>2016</year>
          ). http://arxiv.org/abs/1606.06357
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <surname>Chengyu</surname>
            <given-names>Wang</given-names>
          </string-name>
          , Rong Zhang, Xiaofeng He, and
          <string-name>
            <given-names>Aoying</given-names>
            <surname>Zhou</surname>
          </string-name>
          .
          <year>2016</year>
          .
          <article-title>Error Link Detection and Correction in Wikipedia</article-title>
          .
          <source>In Proceedings of the 25th ACM International on Conference on Information and Knowledge Management (CIKM '16)</source>
          . ACM, New York, NY, USA,
          <fpage>307</fpage>
          -
          <lpage>316</lpage>
          . https://doi.org/10.1145/2983323.2983705
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <surname>Zhenglu</surname>
            <given-names>Yang</given-names>
          </string-name>
          ,
          <string-name>
            <given-names>Jianjun</given-names>
            <surname>Yu</surname>
          </string-name>
          , and
          <string-name>
            <given-names>Masaru</given-names>
            <surname>Kitsuregawa</surname>
          </string-name>
          .
          <year>2010</year>
          .
          <article-title>Fast Algorithms for Top-k Approximate String Matching</article-title>
          .
          <source>In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI'10)</source>
          . AAAI Press,
          <fpage>1467</fpage>
          -
          <lpage>1473</lpage>
          . http://dl.acm.org/citation.cfm?id=
          <volume>2898607</volume>
          .
          <fpage>2898841</fpage>
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>