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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Recommending Tumblr Blogs to Follow with Inductive Matrix Completion</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Donghyuk Shin</string-name>
          <email>dshin@cs.utexas.edu</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Suleyman Cetintas</string-name>
          <email>cetintas@yahoo-inc.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kuang-Chih Lee</string-name>
          <email>kclee@yahoo-inc.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Dept. of Computer Science, University of Texas at Austin</institution>
          ,
          <addr-line>Austin, TX, 78721</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Yahoo Labs</institution>
          ,
          <addr-line>Sunnyvale, CA, 94089</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2014</year>
      </pub-date>
      <abstract>
        <p>In microblogging sites, recommending blogs (users) to follow is one of the core tasks for enhancing user experience. In this paper, we propose a novel inductive matrix completion based blog recommendation method to e ectively utilize multiple rich sources of evidence such as the social network and the content as well as the activity data from users and blogs. Experiments on a large-scale real-world dataset from Tumblr show the e ectiveness of the proposed blog recommendation method.</p>
      </abstract>
      <kwd-group>
        <kwd>Blog Recommendation</kwd>
        <kwd>Inductive Matrix Completion</kwd>
        <kwd>SVD</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. INTRODUCTION</title>
      <p>
        Tumblr1 is one of the most popular microblogging
services where users can create and share posts with the
followers of their blogs. Similar to Twitter2 and di erent from
Facebook3, connections in Tumblr are unidirectional. Unlike
Twitter, users can create longer, richer and higher quality
content in the form of several post types such as text, photo,
quote, link, chat, audio, and video [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Tumblr also supports
liking and reblogging a post as well as attaching tags to it.
      </p>
      <p>
        One of the core problems in microblogging sites is
predicting whether a user will follow a blog or not. In addition to
the user-item interactions (user-item matrix), vast majority
of the existing work either used the social network
information or the textual content/pro les of users and items, and
did not e ectively utilize both types of information. A
recent comprehensive survey of the state-of-the-art methods
can be found in [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. In the case of Tumblr, in addition to
Work was done when the rst author was on a summer
internship with Yahoo Labs.
1www.tumblr.com
2www.twitter.com
3www.facebook.com
the social network information, rich user and blog features
can be extracted from high quality posts as well as like and
reblog graphs from user activities.
      </p>
      <p>
        In this paper, we propose a novel inductive matrix
completion (IMC) based blog recommendation system that e
ectively utilizes the social network as well as the rich content
and activity (network) data from users and blogs in a
unied framework. Although, IMC has been shown to be highly
e ective in other domains such as bioinformatics (e.g., the
gene-disease association problem), it has not been utilized
for recommendation tasks [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. However, IMC has several
advantages over the standard low rank matrix completion
approaches. Speci cally, it overcomes extreme sparsity in the
data by incorporating diverse features of users and blogs
obtained through various sources. Furthermore, it is capable of
making new recommendations even for users or blogs with
very few or unknown following information. Experiments
on real-world proprietary data from Tumblr show that IMC
signi cantly outperforms standard methods for the blog
recommendation task.
2.
      </p>
    </sec>
    <sec id="sec-2">
      <title>METHOD</title>
      <p>
        Formally, let R 2 Rm n be the user-blog follower matrix,
where each row corresponds to a user and each column
corresponds to a blog, such that Rij = 1, if user i is following
blog j and 0 otherwise. The low rank matrix completion
approach is one of the most popular and successful
collaborative ltering methods for recommender systems [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. The
goal is to recover the underlying low rank matrix by using
the observed entries of R, which is typically formulated as
follows:
min X (Rij
W;H (i;j)2
      </p>
      <p>(W HT )ij )2 + 2 (kW k2F + kHk2F );
where W 2 Rm r and H 2 Rn r with r being the dimension
of the latent feature space; is the set of observed entries;
is a regularization parameter.</p>
      <p>
        However, the standard formulation is restricted to the
transductive setting, i.e., predictions can only be made to
existing users and items, and su ers performance with
extreme sparsity in the data. Recently, a novel inductive
matrix completion (IMC) approach was proposed by [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] that
incorporates side information of users and items given in
the form of feature vectors alleviating data sparsity issues
and enabling predictions for new users and items.
Mathematically, IMC is formulated as follows:
      </p>
      <p>xiT W HT yj )2 + 2 (kW k2F + kHk2F );
where xi 2 Rfu and yj 2 Rfb are feature vectors for user i
and item j, respectively (i.e., W 2 Rfu r and H 2 Rfb r).
Given a new blog j, the predictions Rij for each user i can
be calculated with the feature vector yj available. Note
that the number of parameters to learn is (fu + fb) r,
which depends only on the number of user and item features,
whereas there is (m + n) r parameters in the standard
matrix completion.</p>
    </sec>
    <sec id="sec-3">
      <title>EXPERIMENTS</title>
      <p>
        We evaluated IMC for blog recommendation, where
additional side information of both users and blogs are available.
We compare IMC against the standard matrix completion
formulation (MC) as well as the Singular Value
Decomposition (SVD), which has been shown to perform well for top-N
recommendation tasks [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. As a baseline, we also report
results of using a simple global popularity ranking (Global)
for recommendation, where blogs are ranked by the
number of followers. We randomly sampled 1 million users and
100 thousand blogs from the Tumblr follower graph
resulting in 12.5 million follows, i.e., nonzero elements in R. Note
that we retain users and blogs with at least 5 followees and
followers, respectively, and use 10-fold cross-validation for
evaluation.
      </p>
      <p>
        For additional features, we use like, reblog, and tags
information collected over a period of 1 month from Tumblr.
Both like and reblog activities can be represented as a graph
similar to the follower graph R. One way to obtain useful
and robust features is to consider the principal components
of the adjacency matrix corresponding to the like and reblog
graphs. That is, we compute p principal components and
use them as latent user and blog features for IMC. For the
tags used in the posts of each blog, we rst compute vector
representations of each tag using the continuous skip-gram
model [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], which in turn are used to cluster the tags into c
clusters by the k-means algorithm. Using the cluster
information, we create a histogram of the tag's cluster for each
blog as a compact representation of tags used in that blog.
Thus, we have fu = p features for users and fb = p + c
features for blogs, where we use p = 500 and c = 1000 in
the experiments. We use rank r = 100 for SVD and MC,
rank r = 10 for IMC, and set = 0:1, which are determined
using cross-validation.
      </p>
      <p>We measure the recommendation performance using the
F1 score for the top-20 recommendations generated by each
method, which is the region of partical interest for
recommender systems. We also report the AUC (area under the
curve) measured from the precision-vs-recall plot. Results of
the proposed IMC method are shown in comparison to the
baselines, Global, SVD, and MC for both metrics in Table
1. Note that we present normalized (relative) results in both
metrics using the MC method as the baseline.</p>
      <p>
        It is very interesting to see in Table 1 that the simple
Global method ourperforms both SVD and MC baselines.
This can be explained by the facts that most users follow
highly popular blogs such as institutions or celebrities [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]
and that both SVD and MC su er signi cantly from data
sparsity. Table 1 also shows that IMC is the best
performing method out of all methods. This set of results
explicitly shows that IMC succesfully handles data sparsity by
incorporating the rich user and blog data, and signi cantly
improves over MC as well as other methods.
      </p>
    </sec>
    <sec id="sec-4">
      <title>CONCLUSIONS</title>
      <p>Recommending blogs (users) to follow is one of the core
tasks for enhancing user experience in online microblogging
sites such as Tumblr. In addition to the social network
information, it is very important to e ectively utilize the rich
user and blog content (e.g., tags) as well as users' activities
such as like and reblog. This paper proposes a novel
inductive matrix completion based blog recommendation method
that e ectively utilizes the social network as well as rich
content and activity data from users and blogs. Experiments
on large-scale real-world data from Tumblr show the e
ectiveness of the proposed blog recommendation method.</p>
      <p>
        Future work will mainly be conducted in i) utilizing
additional information from users and blogs such as the rich
visual features from posts in Tumblr as well as the (sparser)
textual features, and ii) using probabilistic latent-class or
mixed-membership approaches as shown in [
        <xref ref-type="bibr" rid="ref1 ref2 ref3">2, 1, 3</xref>
        ].
5.
      </p>
    </sec>
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