Recommending Tumblr Blogs to Follow
with Inductive Matrix Completion
Donghyuk Shin
Dept. of Computer Science
University of Texas at Austin
Austin, TX, 78721
[email protected]
Suleyman Cetintas
Kuang-Chih Lee
Yahoo Labs
Sunnyvale, CA, 94089
Yahoo Labs
Sunnyvale, CA, 94089
[email protected]
[email protected]
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 effectively 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 effectiveness of the proposed blog recommendation
Categories and Subject Descriptors
H.2.8 [Database Management]: Database Applications—
Data Mining; H.3.3 [Information Search and Retrieval]:
Information Filtering
Blog Recommendation, Inductive Matrix Completion, SVD
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 different 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 [4]. Tumblr also supports
liking and reblogging a post as well as attaching tags to it.
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
∗Work was done when the first author was on a summer
internship with Yahoo Labs.
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RecSys ’14 Poster Proceedings, October 6-10, 2014, Foster City, CA, USA
of the existing work either used the social network information or the textual content/profiles of users and items, and
did not effectively utilize both types of information. A recent comprehensive survey of the state-of-the-art methods
can be found in [10]. In the case of Tumblr, in addition to
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.
In this paper, we propose a novel inductive matrix completion (IMC) based blog recommendation system that effectively utilizes the social network as well as the rich content
and activity (network) data from users and blogs in a unified framework. Although, IMC has been shown to be highly
effective in other domains such as bioinformatics (e.g., the
gene-disease association problem), it has not been utilized
for recommendation tasks [9]. However, IMC has several advantages over the standard low rank matrix completion approaches. Specifically, 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
significantly outperforms standard methods for the blog recommendation task.
Formally, let R ∈ 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 filtering methods for recommender systems [7]. The
goal is to recover the underlying low rank matrix by using
the observed entries of R, which is typically formulated as
(Rij − (W H T )ij )2 + (kW k2F + kHk2F ),
where W ∈ Rm×r and H ∈ Rn×r with r being the dimension
of the latent feature space; Ω is the set of observed entries;
λ is a regularization parameter.
However, the standard formulation is restricted to the
transductive setting, i.e., predictions can only be made to
existing users and items, and suffers performance with extreme sparsity in the data. Recently, a novel inductive matrix completion (IMC) approach was proposed by [6] 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:
(Rij − xTi W H T yj )2 + (kW k2F + kHk2F ),
where xi ∈ Rfu and yj ∈ Rfb are feature vectors for user i
and item j, respectively (i.e., W ∈ Rfu ×r and H ∈ Rfb ×r ).
Given a new blog ¯j, the predictions Ri¯j for each user i can
be calculated with the feature vector y¯j 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.
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 [5]. 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
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 first compute vector
representations of each tag using the continuous skip-gram
model [8], 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 λ = 0.1, which are determined
using cross-validation.
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.
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 [4]
and that both SVD and MC suffer significantly from data
Table 1: (Normalized) Results of the proposed Inductive Matrix Completion method (i.e., IMC) in
comparison to several baselines.
F1 @20
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 significantly
improves over MC as well as other methods.
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 effectively 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 effectively 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 effectiveness of the proposed blog recommendation method.
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 [2, 1, 3].
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