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  <front>
    <journal-meta />
    <article-meta>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>A. Castellanos</string-name>
          <email>acastellanos@lsi.uned.es</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>A. García-Serrano</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>J. Cigarrán</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>ETSI Informática, UNED. C/Juan del Rosal</institution>
          ,
          <addr-line>16 (Ciudad Universitaria) Madrid</addr-line>
          ,
          <country country="ES">Spain</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2014</year>
      </pub-date>
      <fpage>802</fpage>
      <lpage>812</lpage>
      <abstract>
        <p>This paper summarizes our participation in the CLEF-NEWSREEL 2014 Challenge. The challenge focused on the recommendation of news articles. UNED's participation is in the “Recommend news articles in real-time” task. To address the recommendation tasks, a Formal Concept Analysis framework is proposed to first create the recommendation models and second to compute the recommendations. Our results prove that our FCA proposal outperforms the proposed baseline recommendation approaches. However, its performance is not still enough to be compared to other proposals for this task. In this sense some identified drawbacks, which prejudice the performance of our system, have been identified and possible solutions, to be addressed as future work, have been proposed.</p>
      </abstract>
      <kwd-group>
        <kwd>Formal Concept Analysis</kwd>
        <kwd>Recommendation</kwd>
        <kwd>News Recommender Systems</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In recent times social networks have been the focus of most of the works related to the
management of real-time streams in order to detect, review and characterize events or
produce news reports. This area is especially challenging because even the
best-performing algorithms in a theoretical environment can be useless or inefficient in a real
environment. Experiment-based workshops organized different News
Recommendation Tasks: the International News Recommender Systems Workshop and Challenge
2013 (NRS 2013), the ACM Conferences Series in Recommender Systems 2013
(RecSys 2013), together with contests, such as the plista Contest. The leitmotif of all of
them has been the development of news recommender systems capable of working
online in real environments. However, workshops and challenges not only offer the
possibility to access to a real recommendation scenario, but also allow the evaluation
of the algorithms according to metrics adapted to this context. Some novel works
carried out within this context have been [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] or [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>The CLEF-NEWSREEL offers a recommendation scenario for news articles. The
organizers proposed two tasks: the first propose an offline scenario in which systems
were provided with a collection to train the recommendation algorithms. The second
task proposes a real recommendation scenario (the Online Recommendation Platform)
in which the systems had to respond to the Open Recommendation Platform (ORP)
request.</p>
      <p>
        Our participation in the CLEF-NEWSREEL focuses on Task 2. To address the
challenge proposed in the task, we propose a recommendation algorithm based on Formal
Concept Analysis (FCA). FCA is a mathematical theory that allows content to be
organized. We apply FCA to model items consumed by the users and then offer
recommendations based on this modelling. FCA has been extensively used to model content and
find out unknown knowledge [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. This organization and discovering power has been
applied in recommendation scenarios, although only in preliminary works. The aim of
these works were to take advantage of the high performance of FCA to be able to offer
better recommendations through better item modelling. [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ]. At this point, we propose
the application of FCA for content-based recommendations in a real scenario, taking
advantage of some of the conclusions of the aforementioned works.
      </p>
      <p>The rest of the paper includes the description of the recommendation system, the
experiments carried out and their results, and finally several conclusions are included.</p>
    </sec>
    <sec id="sec-2">
      <title>2. System Description</title>
      <p>In the following, the recommender system developed for our participation in the
CLEFNEWSREEL is detailed. The recommendation proposal follows a content-based
approach: first the content of the items to be recommended (following a FCA approach)
is modelled and secondly a recommendation step is carried out, by selecting “similar”
content to that already consumed by the user.</p>
      <p>2.1</p>
      <sec id="sec-2-1">
        <title>FCA-Based Modelling</title>
        <p>
          The textual information model is reached by means of Formal Concept Analysis (FCA).
FCA is a mathematical theory of concept formation [
          <xref ref-type="bibr" rid="ref6 ref7 ref8 ref9">6-9</xref>
          ] derived from lattice and
ordered set theories that provide a theoretical model to organize formal contexts. A formal
context is defined as a set structure  ∶= ( ,  ,  ), where  is a set of (formal) objects,


a set of (formal) attributes and  a binary relationship between  and  , i.e. (
⊆
×  ), denoted by
        </p>
        <p>, which is read as: the object  has the attribute  . From the
point of view of a content-based recommender system, the FCA formal context can be
seen as a recommendation context, in which the set of objects  is the set of items to
be recommended, the set of attributes</p>
        <p>is a set of textual features, representing the
items, and the binary relationship  can be read as item  has the feature  . By textual
features we refer to the most representative terminology associated to the items.</p>
        <p>
          To set the “representativeness” of each term related to an item, we proposed the
Kullback-Leibler Divergence [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] as a weighting measure, as described in [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. Briefly
explained, we compute the KLD value of the terms in each item by comparing them to
the terms in the rest of the items; the terms with the higher KLD weight (those in the
1st tercile) are then selected as the representatives of the item. An example of this
recommendation context is shown in Table 1.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>Item 1</title>
      </sec>
      <sec id="sec-2-3">
        <title>Item 2</title>
      </sec>
      <sec id="sec-2-4">
        <title>Item 3</title>
      </sec>
      <sec id="sec-2-5">
        <title>Item 4</title>
      </sec>
      <sec id="sec-2-6">
        <title>Feature 1 X X</title>
        <p>From the information reflected in the recommendation context, a set of formal
concepts can be inferred. A formal concept is a pair ( ,  ) where  ⊆  is a set of objects
(the extent of the formal concept) and  ⊆  is a set of attributes (the intent of the
formal concept), which has the following properties:
 If an object  in  is tagged with an attribute  , then  must is included in  (i.e. =
  the intent of the formal concept includes all the attributes shared by the objects in
the extent).
 Conversely, if an object  is tagged with all the attributes in  , then  must be
included in  (i.e.,  =   : the extent of the formal concept includes all those objects
filtered out by the intent).</p>
        <p>To exemplify that, given the Formal Context in Table 2, the following Formal
Concepts will be generated:</p>
        <p>Formal concepts can be formally ordered in a subconcept-superconcept-
relationship in accordance with their extents:</p>
        <p>
          ( , B) ≤ ( ’, B’): (A, B)  (A’, B’)  A  A’
where ( ’, B’) is called a super-concept of ( , B) and, conversely, ( , B) is a
subconcept of ( ’, B’) (i.e., ( , B) is more specific than ( ’, B’)). The order that results can
be proven to be a lattice, which is called the concept lattice, denoted as ℬ ( ,  ,  ),
associated to the formal context. Since concept lattices are ordered sets, they can be
naturally displayed in terms of Hasse diagrams [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ].
        </p>
        <p>
          In a Hassediagram:
 There is exactly one node for each formal concept.
 If C  C’, then C’ is placed above C (C is a sub-concept of C’ or C’ is a super-concept
of C).
 If C  C’ but there is no other intermediary concept C’ such as C  C’’  C’, there is a
line joining C and C’.
The idea followed by the recommendation approach is along the lines of that proposed
in [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ]. The rationale is to take advantage of the relationships represented in the
structure of the concept lattice to find suitable recommendations. Based on the FCA lattice,
a content-based recommendation algorithm has been developed. The first step is the
modelling of the items and second to recommend items similar to those already
consumed by the users [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ].
        </p>
        <p>We have selected this approach because, in our view, a content-based approach
appears to be the most suitable in the given context (news recommendations). In other
contexts, such as movie recommendation, it is not clear whether the content of the items
(e.g. the plot of the movies) is the main signal to get the user’s interest (i.e. the user
might like the movie because of the characters, director, special effects, etc., or the user
interest could be related to some other issues such as the novelty of the movie or a direct
recommendation of another user). However, even though other aspects might be also
related, in news recommendation the content is the most important feature of an item
on identifying the interest of the users. Several other aspects not directly related to the
content but to the recommendation context (e.g. novelty or popularity) are taken into
account (see Section 3.2 where the experimental setup is explained).</p>
        <p>The algorithm bases its operation on a navigation process across the lattice.
Basically, given a target item, the algorithm looks for the most similar items to offer as
recommendations; the algorithm takes the items already consumed by the user and
offers similar items as recommendations. The navigation process starts at the object
concept of the target item in the lattice. The object concept ( ) of  is the most specific
concept (the smallest concept) including  in its extent. The object concept is selected
as the starting point because it is the most specific formal concept (the one with the
most attributes in the intent; that is, the one with the most information) in which the
target item is included. The rationale is that the more information you have about an
item the more accurate will be the recommendation based on similar items.</p>
        <p>The navigation process is carried out by taking the son concepts: the sub-concepts
(i.e. those linked immediately below in the lattice) of the target; and the brother
concepts: the son concepts of the parent concepts (i.e. those linked immediately above in
the lattice) of the target, except the target itself. The navigation is carried out as an
iterative process, fixed by an N value that sets the number of levels that the algorithms
should visit (up and down). All the items, still not consumed by the user, and belonging
to the formal concepts included in the navigation path, are offered as recommendations.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Experiments and Results</title>
      <p>Our participation in the CLEF-NEWSREEL is presented in the following. We finally
participated only in Task 2, by applying the aforementioned FCA modelling and
recommendation proposal, adapted to the specific requirements of the task.
3.1</p>
      <sec id="sec-3-1">
        <title>Task Definition and the ORP</title>
        <p>The task is based on the scenario of news recommendation in real-time. This scenario
is especially challenging, beyond the specific requirements of the recommendation
systems, it includes other issues such as: a high response speed is essential, scalability to
be able to manage the real-time data stream, the ability to compute recommendation
models in real-time to adapt them to the continuous information stream and to integrate
them into the recommendation approach.</p>
        <p>The scenario proposed for the task is the Open Recommendation Platform (ORP),
operated by plista. ORP provides a framework in which the recommendation algorithms
can be deployed. Subsequently, the servers will request recommendations from the
systems. The ORP also provides an evaluation framework based on a real user study, based
on the real interactions of the plista users with the recommendations offered. The
evaluation will focus on click events: the absolute number of clicks and the relative number
of clicks to recommendation requests.
3.2</p>
      </sec>
      <sec id="sec-3-2">
        <title>Experimentation.</title>
        <p>The experimentation focuses on testing the performance of the proposed FCA-based
approach in a real recommendation scenario. Besides the aforementioned problems
related to the real-time issue, there is another problem related to this scenario: the system
has no previous information on the items or users at the beginning. The system should
record all the information coming in to it (new users, new items, new item contents and
new interactions) in order to compile background information to offer
recommendations.</p>
        <p>However, a problem arises in this situation: How much information should the
system store? In principle, it might be thought that the more information stored, the better
the performance of the system. However, this approach has some disadvantages. First
of all, there is the problem of how to manage such a large amount of data. Given that
recommendations should be made in real time, it is not possible to compute such an
amount of data online: as can be seen in Fig.2Fig.5, the systems should process between
12 and 35 thousand requests per day. Furthermore, the systems should also store and
process the information related to these interactions. So, only offline computation is
suitable in order to create a recommendation model. However, even offline
computation is too expensive in terms of complexity. In this sense, instead of considering all the
data, we propose two approaches: 1) consider the most novel 1,000 items, or 2) consider
the top 1,000 scored items at the moment of computing the lattice.</p>
        <p>Another disadvantage is related to the time dimension. Not all the data have the same
importance: it is reasonable to think that the most novel (i.e. the latest data to arrive at
the system) or the top scored (i.e. the data most consumed by the users) is more
interesting for the users. Taking into account both the complexity problem and the time
dimension, we decided take into account only the data belonging to the last previous 24
hours for the recommendation computation (i.e. every 24 hours the previous
information is removed and a new FCA computation on the new data is carried out). But,
considering that some information could be considered interesting for the users from
day to day, the system keeps the most consumed items (the top 100) for the next day.</p>
        <p>In the ORP scenario, the systems were requested to offer recommendations for a
recommendation request. Both the ORP system and the challenge provide a common
framework for the participants in the task in order to compare the system’s
performance. However to measure the suitability of our system, we also developed two
baseline systems to show the improvement in the results due to the application of FCA. It
is important to note that, both for the baselines and for the FCA based approach the
input data is the same (the data of the last 24 hours plus the top scored items).
 Baseline 1 - Most Novel Items: Given a recommendation request, this system uses
the set of most novel items; that is the last item that has arrived at the systems.
 Baseline 2 - Top Scored Items: Given a recommendation request, this system offers
the set of top scored items. The score of an item is set by the number of times that it
has been accessed or it has been clicked, when it has been offered as
recommendation.
 Approach 1: FCA-Based Recommendation – Most Novel: To address the
requests, the recommendation scenario proposed in Section 0 has been applied. That
is, given a recommendation request, the item contained in the request is used for the
system to look for similar items in the lattice structure. The information is updated
daily based on the most novel items.
 Approach 2: FCA-Based Recommendation–Top Scored: To address the requests,
the recommendation scenario proposed in Section 0 has been applied. That is, given
a recommendation request, the item contained in the request is used for the system
to look for similar items in the lattice structure. The information is updated daily
based on the top scored items.
3.3</p>
      </sec>
      <sec id="sec-3-3">
        <title>Results</title>
        <p>The official results are shown in the following. Note that our systems were deployed
for the whole month (May). However, the first weeks were only for development and
debugging.</p>
        <p>The results presented here correspond to the last weeks, when the systems were
really in the production phase. Fig.2 and Fig.3 show the results of both baselines. The
behavior of both is similar, however the results of the one based on most novel items
outperform those of the approach based on the top scored. It points out that users prefer
a novel although not-so-accurate recommendation.</p>
        <p>Once the baseline performance of the system has been outlined, the performance of
the FCA-based approach is presented in Fig.4 and Fig.5. Note that Fig.4 has a time
deviation with respect to other figures, due to problems with the computation of this
approach. However the results can still be compared to the previous ones given that 1)
the system, 2) the environment and 3) the amount of data processed is the same for all
the approaches. The first point to highlight is that both approaches outperform their
baselines (compare Fig.4 and Fig.2 for the most novel-based approaches and compare
Fig.5 and Fig.3 for the top score-based approaches). As was highlighted in the previous
results, the most novel-based approach again improves the results of the top scored.
The previous analysis is only based on the comparison between our different
approaches. Comparing our results with the rest of the participants in the task, it can be
seen that our results (in bold) do not reach the general performance of the task (Table
3).</p>
        <p>As regards these results, firstly note that they combine the performance of all of our
approaches and, consequently, the results are downgraded by the baselines. However,
even taking the top-performing approach (FCA Based Recommendation – Top Scored),
our results will not be among the best. During the experimentation we identified two
aspects that could explain these results:
 The need for a larger amount of information: In the experimentation section we
argued for the need to limit the amount of information to be computed in order to
generate the recommendations. In this sense we only had to compute the 1,000 most
suitable items. This number was set by our limitation in computing the lattices. A
more extended item set to be taken into account to compute the lattices could lead to
a more informative representation and, consequently, a more accurate
recommendation.
 The time lag in the lattices: The lattices were computed daily; that is, every day the
most suitable items of the previous day were used in the computations. It meant that
the recommendations had a one-day lag. If this lack of novelty were solved, the
performance of the system might be better.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusions</title>
      <p>To address the recommendation of news articles in real-time task, based on the ORP
Platform, a recommendation approach based on Formal Concept Analysis has been
presented. The aim of this work was to take advantage of the high performance of the
FCA in content modelling to apply it to a recommendation task.</p>
      <p>To take the special requirements of this real-time environment into account and to
be able to compute recommendations in the required time, our framework proposes a
daily item modelling to create an FCA-based item modelling. This item modelling is
used to look for similar items that related to the recommendation request. Some issues
such as novelty and diversity have been also taken into account as explained.</p>
      <p>For the experimentation, we computed two baselines covering two basic
recommendation proposals: most-novel and top-scored items. Based on these two baselines we
presented two FCA-based proposals, which are promising compared to our baselines.
However if we take a look at the results of the other the participants, our FCA-based
system does not reach the overall performance. In this sense, two aspects which
prejudice our performance were identified: the need to use more data to create our
FCAbased item representation and the need to solve the time lag. To sum up, we
demonstrated the viability of FCA to be applied in such a challenging scenario, even if it is
still far from the performance of the state-of-the-art systems in this field.</p>
      <p>As regards the latter, some lines of future work come about. The main aspect to be
addressed is related to solving the complexity problems of our approach. In this sense
we are on the way to developing a FCA Big Data Framework, in order to take into
account and compute the entire amount of data available in this kind of environment.
In our approach, the FCA computation represents a bottleneck, even more so when the
amount of data becomes as large as it does in this scenario. As a solution, we propose
to select only some data (according to a criterion) to create the FCA models. It leads to
a loss of knowledge related to this loss of data. A Big Data Framework would allow
much more data to be computed, ideally leading to more informative models which
could create more accurate recommendations.</p>
      <p>Another issue to be addressed is the time lag problem. This aspect does not have
such a direct solution; it could be addressed: 1) by taking a smaller time snapshot to
compute the modelling, 2) by adapting the computation time to several variables (i.e.
the amount of data available or period of the day), or 3) by applying a smoothing
process in the removal of old data.</p>
      <p>Acknowledgments. This work has been partially supported by MA2VIRMR
(S2009/TIC-1542), and HOLOPEDIA (TIN 2010-21128-C02) Spanish projects.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          1.
          <string-name>
            <surname>Said</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Bellogín</surname>
          </string-name>
          , A. and
          <string-name>
            <surname>de Vries</surname>
          </string-name>
          , A.:
          <article-title>News Recommendation in the Wild: CWI's Recommendation Algorithms in the NRS Challenge</article-title>
          .
          <source>In: Proceedings of the International News Recommender Systems Challenge (NRS</source>
          <year>2013</year>
          ),
          <source>at the 7th ACM Conference on Recommender Systems (RecSys</source>
          <year>2013</year>
          ).
          <article-title>(</article-title>
          <year>2013</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          2.
          <string-name>
            <surname>Garcin</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Faltings</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          :
          <article-title>Pen recsys: A personalized news recommender systems framework</article-title>
          .
          <source>In: Proceedings of the 7th ACM Conference on Recommender Systems. RecSys '13</source>
          , New York, NY, USA, ACM (
          <year>2013</year>
          )
          <fpage>469</fpage>
          -
          <lpage>470</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          3.
          <string-name>
            <surname>Poelmans</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Elzinga</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Viaene</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Dedene</surname>
          </string-name>
          , G.:
          <article-title>Formal concept analysis in knowledge discovery: a survey</article-title>
          .
          <source>In: Proceedings of the 18th international conference on Conceptual structures: from information to intelligence</source>
          .
          <source>ICCS'10</source>
          , Berlin, Heidelberg, Springer-Verlag (
          <year>2010</year>
          )
          <fpage>139</fpage>
          -
          <lpage>153</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          4.
          <string-name>
            <surname>Ignatov</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kaminskaya</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Bezzubtseva</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Konstantinov</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Poelmans</surname>
          </string-name>
          , J.:
          <article-title>FCA-Based Models and a Prototype Data Analysis System for Crowdsourcing Platforms</article-title>
          . In Pfeiffer, H.,
          <string-name>
            <surname>Ignatov</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Poelmans</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Gadiraju</surname>
          </string-name>
          , N., eds.:
          <article-title>Conceptual Structures for STEM Research and Education</article-title>
          . Volume
          <volume>7735</volume>
          of Lecture Notes in Computer Science. Springer Berlin Heidelberg (
          <year>2013</year>
          )
          <fpage>173</fpage>
          -
          <lpage>192</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          5.
          <string-name>
            <surname>Li</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Murata</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          :
          <article-title>A knowledge-based recommendation model utilizing formal concept analysis and association</article-title>
          . In: Computer and Automation Engineering (ICCAE),
          <source>2010 The 2nd International Conference on. Volume</source>
          <volume>4</volume>
          . (
          <year>2010</year>
          )
          <fpage>221</fpage>
          -
          <lpage>226</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          6.
          <string-name>
            <surname>Belohlavek</surname>
          </string-name>
          , R.:
          <article-title>Introduction to formal concept analysis</article-title>
          .
          <source>Olomouc</source>
          ,
          <string-name>
            <surname>UPOL</surname>
          </string-name>
          , Faculty of Science, Department of Computer Science (
          <year>2008</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          7.
          <string-name>
            <surname>Ganter</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Wille</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Franzke</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          :
          <article-title>Formal concept analysis</article-title>
          :
          <source>mathematical foundations</source>
          . Springer-Verlag New York, Inc. (
          <year>1997</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          8.
          <string-name>
            <surname>Wille</surname>
          </string-name>
          , R.:
          <article-title>Concept lattices and conceptual knowledge systems</article-title>
          .
          <source>Computers &amp; mathematics with applications 23(6)</source>
          (
          <year>1992</year>
          )
          <fpage>493</fpage>
          -
          <lpage>515</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          9.
          <string-name>
            <surname>Wille</surname>
          </string-name>
          , R.:
          <source>Restructuring Lattice Theory: An Approach Based On Hierarchies Of Concepts</source>
          . Volume
          <volume>5548</volume>
          of Lecture Notes in Computer Science. Springer Berlin Heidelberg (
          <year>2009</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          10.
          <string-name>
            <surname>Kullback</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Leibler</surname>
            ,
            <given-names>R.A.</given-names>
          </string-name>
          :
          <article-title>On information and sufficiency</article-title>
          .
          <source>The Annals of Mathematical Statistics</source>
          <volume>22</volume>
          (
          <issue>1</issue>
          ) (
          <year>1951</year>
          )
          <fpage>79</fpage>
          -
          <lpage>86</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          11.
          <string-name>
            <surname>Castellanos</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          :
          <article-title>Recomendación de contenidos digitales basada en divergencias del lenguaje diseño experimentación y evaluación</article-title>
          .
          <source>Master'sthesis, UNED</source>
          (
          <year>2013</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          12.
          <string-name>
            <surname>du</surname>
            Boucher-Ryan,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Bridge</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          :
          <article-title>Collaborative recommending using formal concept analysis</article-title>
          .
          <source>Knowledge-Based Systems 19(5)</source>
          (
          <year>2006</year>
          )
          <fpage>309</fpage>
          -
          <lpage>315</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          13.
          <string-name>
            <surname>Ricci</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Shapira</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          :
          <article-title>Recommender systems handbook</article-title>
          . Springer (
          <year>2011</year>
          )
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>