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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Removing Bad Influence: Identifying and Pruning Detrimental Users in Collaborative Filtering Recommender Systems</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Philipp Meister</string-name>
          <email>philipp.meister@student.uni-siegen.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lukas Wegmeth</string-name>
          <email>lukas.wegmeth@uni-siegen.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Tobias Vente</string-name>
          <email>tobias.vente@uni-siegen.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Joeran Beel</string-name>
          <email>joeran.beel@uni-siegen.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Intelligent Systems Group, University of Siegen</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Recommender systems commonly employ Collaborative Filtering to generate personalized recommendations, forming an implicit social network where users influence each other's recommendations based on their preferences. In this paper, we show that it is possible to identify users with detrimental influence-those who negatively afect the recommendations of others-and that merely removing specific detrimental users from the training data can improve system performance. We apply a Leave-one-out analysis across five datasets to capture how recommendations change if a specific user is removed. Based on that data, we quantify positive and negative influences and implement a pruning strategy to remove detrimental users. Importantly, our strategy still provides recommendations to the pruned users by recommending the most popular items. We evaluate our pruning strategy on five commonly used datasets, including MovieLens, Amazon, and LastFM. We show that pruning detrimental users increases kNN performance, achieving an average performance increase of 3% for Item-Item kNN while removing 3.56% of users from the training data. Our findings highlight the potential of influence-based pruning to enhance recommender systems by increasing performance and creating resilience against detrimental influence.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Collaborative Filtering</kwd>
        <kwd>Recommender Systems</kwd>
        <kwd>User Influence</kwd>
        <kwd>User Pruning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Collaborative Filtering (CF) algorithms make
recommendations based on the principle that users who agree on the
same items will do so in the future. The result is a system
in which each user’s recommendations are primarily
determined by their similarity to other users. Due to users’
influence on each other, Lathia et al. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] interpret kNN CF
recommender systems as implicit social networks. Much
like in a social network, users’ influence varies widely,
resulting in a few users who significantly impact the overall
system’s behavior [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. For our analysis, we define a user’s
influence as their ability to change other users’
recommendations with their ratings.
      </p>
      <p>
        In the quest to increase the performance and robustness
of recommender systems, those influential users [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] are an
important asset for recommender system engineers. For
example, influential users can improve recommendations by
rating new items, thereby addressing the cold start problem
for those items [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. On the other hand, bad actors, e.g.,
users with fake profiles or users who inject fake ratings to
push certain items, could exploit the power of influential
users and hurt recommendations. Wilson et al. [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] find that
depending on the dataset and algorithm, using just 1% of
users for such an attack results in significant performance
reductions.
      </p>
      <p>
        The potential of influential users to either enhance or
erode the quality of recommendations leads us to an
intriguing possibility. We hypothesize that there are real users
in the training data whose inclusion negatively impacts
the recommendations for other users and that removing
these users can improve overall system performance. We
call them detrimental users. Intuitively, removing many
or all detrimental users should improve recommendations.
However, it is a common assumption that less training data
decreases performance [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], so removing many detrimental
users may hurt rather than increase performance. To
investigate whether detrimental users exist and how removing
them afects recommendations, we examine the following
research question:
      </p>
      <p>RQ: How can we identify and separate detrimental
users?
To answer our research question, we analyze the influence
of every individual user in five popular datasets using three
CF kNN and matrix factorization algorithms to quantify
user influence on ranking predictions. We show that it is
possible to identify detrimental users who negatively impact
the performance of other users and that pruning the most
detrimental users can improve overall recommendations.</p>
      <p>
        The source code reproducing all the results presented in
this paper is available at our GitHub1.
Several aspects of user influence in recommender systems
have been the subject of previous research. Rashid et al.
[
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] propose a general approach to determine user influence
in rating-based recommender systems and analyze
UserUser and Item-Item CF systems using the Hide-one-User or
Leave-one-out method. They discover correlations between
user influence and several simple heuristics and use them
to create a regression model to estimate user influence. The
model predictions have a squared correlation coeficient of
0.94 for User-User and 0.99 for Item-Item, indicating that
simple heuristics can estimate influence. Morid et al. [ 7]
discover similar influence heuristics employing the same
approach as Rashid et al. [8]. However, neither approach
distinguishes between positive and detrimental influence.
      </p>
      <p>
        In more recent work, Eskandanian et al. [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] study
influential users in CF systems across diferent domains. Their
analysis shows that the efect of influence is generally more
substantial in matrix factorization systems compared to
kNN, and several factors, including centrality, number of
ratings, and similarity to the average user, can identify
inlfuential users. Furthermore, they find that the efect of
influence depends on the parameters like features for
matrix factorization. Like Rashid et al. [
        <xref ref-type="bibr" rid="ref6">6, 8</xref>
        ], the influence
discrimination model used for the underlying analysis does
not account for positive or negative influence, making it
impossible to identify detrimental influential users.
      </p>
      <p>
        Wilson et al. [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] discover that it is possible to hurt CF
kNN recommender systems by conducting a targeted power
user attack. In contrast, Seminario et al. [9] study the same
for matrix factorization CF. In this context, power users
are synonymous with our definition of influential users.
They find that when power users are injected with biased
ratings for new items, the MAE for User-User CF rises by
up to 3% on the MovieLens 1M dataset [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. This could imply
that influential users harm recommendations depending on
their rating profile. Additionally, their results show that
Item-Item kNN is less vulnerable to power user attacks than
User-User kNN and matrix factorization.
      </p>
      <p>
        Existing research indicates that just a few influential users
have the potential to considerably change
recommendations [
        <xref ref-type="bibr" rid="ref3 ref6">6, 3, 9</xref>
        ], both positively and negatively. We expand
on previous research by using implicit feedback data, e.g.,
unweighted user interactions, and interpreting influence as
a multi-dimensional metric. Furthermore, we distinguish
between positive and detrimental influence and study how
detrimental users can be identified and how pruning them
afects recommender system performance.
      </p>
    </sec>
    <sec id="sec-2">
      <title>3. Method</title>
      <p>
        We examine detrimental users and their efect on
recommendations in two parts. The first consists of a user influence
analysis, which aims to identify detrimental influential users
by quantifying influence via diferent metrics. To achieve
this, we adopt the Leave-one-out (LOO) concept described
by Rashid et al. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] and developed a pipeline to capture
influence data for every user. In the second part of the analysis,
we use the obtained influence data to study how pruning
users from the training data based on diferent influence
metrics changes performance. One important remaining
issue is that pruning removes valuable training data and
disregards pruned users, which Beel et al. [10] identified
as a widespread problem in recommender system research.
To avoid that, we do not simply remove pruned users but
instead calculate their recommendations separately,
recommending the most popular items.
      </p>
      <p>We use five datasets in our analysis: ML-100k, ML-1M
[11], Last.FM [12], Amazon-Digital-Music and
AmazonLuxury-And-Beauty [13]. We transform explicit feedback
data, e.g., ratings, into implicit feedback data, e.g.,
interactions, treating every rating as a positive interaction and
evaluate the NDCG@10 of User-User kNN, Item-Item kNN,
and Alternating Least Squares (ALS) CF on each dataset. We
use the algorithm implementations of LensKit [14].</p>
      <p>The first part of our analysis follows a simple question:
if one specific user is removed from the training data, how
does the NDCG@10 change for every other user? To answer
this question, we implement the following LOO pipeline.
First, we calculate the baseline result for each algorithm, e.g.,
the NDCG@10 performance of each algorithm considering
all users. From the obtained results, we build a vector b,
with each entry  representing the baseline NDCG@10 for
a user . Then, we prune the user  from the training and
test data. We train a new model and calculate the
recommendations on this pruned data. These results form a vector
r for each pruned user , with , being the NDCG@10 for
user  calculated without user  in the training data. The
NDCG@10 of the pruned user  is set to 0 because the user
receives no recommendations. The basis of the influence
analysis is the diference between the pruned results r and
baseline results b. For every user , a vector ∆ r = r − b
describes this diference. Pruning successively every user 
results in a Matrix  with</p>
      <p>= (∆ r)=1,...,
where  is the total number of users in the dataset. If for
users  and  ∆ , &gt; 0 holds, user  receives better
recommendations when user  is not in the training data, ergo
user  has a detrimental influence on user . Conversely,
if ∆ , &lt; 0 holds, the existence of user  in the data
improves user ’s recommendations. Using , we calculate
the following four normalized influence metrics.</p>
      <p>
        The influence mean  is the diference between the
baseline and pruned mean NDCG@10. It describes how the
overall system performance changed compared to the
baseline performance due to pruning the user . A feature of  
is that it depends on user ’s baseline performance because
’s performance on the pruned dataset is 0. To address this
issue, we introduce the cleaned influence mean  , which
removes the pruned user  from the influence mean
calculations. Furthermore, we introduce the influence diference
 , which we derive from the    metric presented by
Rashid et al. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. It calculates the diference between the
number of users influenced positively and negatively by user
. Finally, the influence score  accounts for the cleaned
influence mean and the influence diference by calculating
their diference with  =  −  .
      </p>
      <p>To test whether pruning multiple detrimental users from
the training data based on the acquired influence data
improves recommendations, we evaluate an optimal pruning
strategy on all datasets and algorithms using user-based
ifve-fold cross-validation. We use random search to identify
the optimal pruning threshold of each influence metric for
each dataset and algorithm and prune users based on this
optimal pruning strategy.</p>
    </sec>
    <sec id="sec-3">
      <title>4. Results &amp; Discussion</title>
      <p>The result of pruning detrimental users is illustrated in
Figure 1. Item-Item kNN benefits the most with an
average performance increase of 3% while User-User kNN
also shows improvements but on a lower level with around
0.2%. ALS is, on average, negatively afected by pruning
detrimental users. The relative performance change for
the users remaining in the training data is, on average,
around 0.5 percentage points better than all users
combined. This is expected since the pruned users are
recommended the most popular items, which are worse than CF.</p>
      <p>The amount of pruned users varies significantly
depending on the dataset. Table 1 shows an average, with over
3.5% of users pruned for Item-Item kNN, confirming that
removing multiple detrimental users can improve
recommendations despite reducing the training data. We observe
that the optimal influence metric and threshold depend on
the dataset and algorithm. The performance increase in our
experiments varies depending on the dataset, with larger
datasets benefitting more. For example, we observe a three
times higher relative performance improvement for ML-1M
than ML-100K.</p>
      <p>To illustrate, Figure 2 shows the user distribution in the
ML-1M dataset using Item-Item kNN. The dispersion of the
influence score increases with rising influence. This leads
to some influential users significantly negatively afecting
other users. Pruning all users below the threshold shown
in Figure 2 leads to a considerable overall performance
improvement of over 7% for ML-1M Item-Item kNN.</p>
      <p>The results from our pruning analysis answer our initial
research question by confirming that the influence metrics
we introduce can identify and diferentiate users with
positive and detrimental influences. The performance
improvement we observe, especially for Item-Item kNN,
demonstrates that the users we identify as detrimental harm the
recommendations of other users. However, this efect
depends on the algorithm, as shown by the reduced
performance of ALS when pruning users. Future work should
focus on understanding the characteristics of detrimental
users and try to identify them based on heuristics
without the need to conduct a computationally expensive LOO
analysis.
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