<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Microposts</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>H G - R A N K: A Hypergraph-based Keyphrase Extraction for Short Documents in Dynamic Genre</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Abdelghani Bellaachia</string-name>
          <email>bell@gwu.edu</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>∗This author is sponsored by King Saud University, Saudi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mohammed Al-Dhelaan∗</string-name>
          <email>mdhelaan@gwu.edu</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Arabia</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Computer Science, The George Washington University</institution>
          ,
          <addr-line>Washington, DC 20052</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2014</year>
      </pub-date>
      <volume>4</volume>
      <fpage>42</fpage>
      <lpage>49</lpage>
      <abstract>
        <p>Conventional keyphrase extraction algorithms are applied to a fixed corpus of lengthy documents where keyphrases distinguish documents from each other. However, with the emergence of social networks and microblogs, the nature of such documents has changed. Documents are now of short length and evolve topics which require specific algorithms to capture all features. In this paper, we propose a hypergraphbased ranking algorithm that models all the features in a random walk approach. Our random walk approach uses weights of both hyperedges and vertices to model short documents' temporal and social features, as well as discriminative weights for word features respectively, while measuring the centrality of words in the hypergraph. We empirically test the effectiveness of our approach in two different data sets of short documents and show that our approach has an improvement of 14% to 25% in precision over the closest baseline in a Twitter data set and 10% to 27% in the Opinosis data set.</p>
      </abstract>
      <kwd-group>
        <kwd>Text hypergraphs</kwd>
        <kwd>Keyphrase extraction</kwd>
        <kwd>Random walks</kwd>
        <kwd>Short documents</kwd>
        <kwd>Hypergraph random walks</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>I.2.7 [ARTIFICIAL INTELLIGENCE]: Natural
Language Processing—Text analysis</p>
    </sec>
    <sec id="sec-2">
      <title>1. INTRODUCTION</title>
      <p>Short text messages are ubiquitous nowadays in social
networks and across the web. Regardless of the length
limitation, the size restriction did not limit the popularity of
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online
republish, to post on servers or to redistribute to lists, requires prior specific
p#eMrmicisrsoiponosatnsd2/0o1r4a, fAeep.ril 7th, 2014, Seoul, Korea.</p>
      <p>Copyright 20XX ACM X-XXXXX-XX-X/XX/XX ...$15.00.
social interaction through such messages. Twitter, for
instance, has more than 200 million active users each month1.
Such high popularity necessitates ranking systems capable
of measuring the importance of keywords and keyphrases
within such limited length to facilitate search, indexing, and
detecting trends. By finding salient terms, tasks such as
summarization and text visualization become feasible.
However, the dynamic nature of social microblogs makes ranking
a non-trivial task.</p>
      <p>Microblogs have a dynamically changing content that needs
specially designed algorithms for keyphrase extraction.
Descriptive keyphrases are keyphrases that signify topics in a
document and help differentiate it from other documents in
the corpus. However, the social aspects and evolution of
topics in a social media genre make it rather difficult to find
keyphrases. Most keyphrase extraction algorithms do not
account for the temporal and social attributes when finding
keyphrases since they are designed for static documents
corpora. Therefore, a number of interesting research questions
arise in social microblogs where topics change frequently. If
the content is dynamically changing, then can we rely on
conventional keyphrases extraction approaches? How can
we account for the temporal and social attributes in social
media for keyphrase extraction?</p>
      <p>In this article, we present a hypergraph-based algorithm,
called HG-Rank, that is capable of modeling temporal and
social aspects in addition to discriminative weights. A
hypergraph is a generalization of graphs were edges have a set
of vertices (called hyperedges) instead of two nodes. We
define a lexical hypergraph where vertices are distinct words
and hyperedges are short documents that contain the words.
We model the temporal and social attributes of documents
as hyperedge weights to reflect the attributes over the
document’s keywords, and we model discriminative term weights
as vertex weights to give the model the ability of recognizing
topical terms. We design a weighted random walk over the
hypergraph to measure the centrality of keywords taken into
account all the aforementioned features.</p>
      <p>
        To rank vertices in a hypergraph, we generalize a
probabilistic random walk suitable for a weighted hypergraph
structure. The surfer considers the weights of both
vertices and hyperedges for transitioning. The intuition is that
the surfer will prefer words that has the following
properties. The words belong to a recent document, and they
exist in a document that has attracted social users, for
in1https://twitter.com/twitter/status/281051652235087872
keyphrase ranking over hypergraphs based on Zhou et al.[
        <xref ref-type="bibr" rid="ref30">29</xref>
        ]
defintions. They proposed using semantic connection
between phrases(vertices) to form hyperedges using external
knowledge sources as in Wikipedia. Our work is different in
the following matter: we use a completely unsupervised
approach for ranking keywords instead of sentences or phrases
which may not be easy to find in social snippets, we
propose a new weighted random walk that uses both
hyperedges and vertices weights, and we include temporal and
social attributes in the ranking. Finally, unlike exciting
approaches for semi-supervised hypergraph ranking our
ranking approach is query independent and thus unsupervised.
3.
      </p>
    </sec>
    <sec id="sec-3">
      <title>NOTATIONS AND DEFINITIONS</title>
      <p>Let HG(V, E) be a hypergraph with the vertex set V and
the set of hyperedges E. A hyperedge e is a subset of V where
∪e∈E e = V . Let HG(V, E, w) be a weighted hypergraph
where w : E → R+ is the hyperedge weight. A hyperedge e
is said to be incident with v when v ∈ e. A hypergraph has
an incidence matrix H ∈ R|V |×|E| as follows:
The vertex and hyperedge degree are defined as follows:
h(v, e) =
(1 if v ∈ e</p>
      <p>0 if v ∈/ e
d(v) =</p>
      <p>X w(e)h(v, e)
δ(e) =</p>
      <p>X h(v, e) = |e|
e∈E
v∈V
stance re-tweet in Twitter. Additionally, the surfer will
prefer topically discriminative words capable of finding accurate
keyphrases.</p>
      <p>The contribution of this paper can be summarized as
follows:
• We propose a new hypergraph approach to jointly model
temporal and social features within the hypergraph
structure. This model is capable of recognizing the
importance of time and social features that are
important in a dynamic genre.
• The hypergraph-based HG-Rank algorithm is the first
graph-based approach for keyphrase extraction that
considers the high-order relation between words
instead of a pair-wise relation as in conventional
graphbased keyphrase extraction.
• We evaluate our approach with two different data sets
Twitter and Opinosis. We show the effect of each
dimension on the task of keyphrase extraction.</p>
      <p>The rest of the paper is organized as follows. A discussion
of the related work is in Section 2. We define the
hypergraph notation needed for explaining the proposed approach
in Section 3. The proposed approach will be thoroughly
explained in Section 4. Section 5 will describe the data and
experimental results. The paper conclusion is in Section 6.
2.</p>
    </sec>
    <sec id="sec-4">
      <title>RELATED WORK</title>
      <p>Our work is related to three different research areas, namely:
temporal and social aspects for keyphrase extraction,
graphbased keyphrase extraction, and hypergraphs. This work
bridges such areas for the task of keyphrase extraction in a
unified framework.</p>
      <p>
        The emergence of social networks has motivated researchers
to examine the inclusion of temporal and social dimensions
into search [
        <xref ref-type="bibr" rid="ref28">27</xref>
        ][
        <xref ref-type="bibr" rid="ref17">16</xref>
        ][
        <xref ref-type="bibr" rid="ref14">13</xref>
        ], summarization[
        <xref ref-type="bibr" rid="ref25">24</xref>
        ][
        <xref ref-type="bibr" rid="ref24">23</xref>
        ], and keyphrase
extraction[
        <xref ref-type="bibr" rid="ref29">28</xref>
        ][
        <xref ref-type="bibr" rid="ref12">11</xref>
        ]. Yu et al. proposed to combine the
temporal dimension into a PageRank[
        <xref ref-type="bibr" rid="ref7">6</xref>
        ] approach for ranking
research publications considering their publication time[
        <xref ref-type="bibr" rid="ref28">27</xref>
        ].
Wan proposed a time-aware summarization algorithm over
a lexical graph[
        <xref ref-type="bibr" rid="ref25">24</xref>
        ]. A probabilistic approach for
personalized temporally-aware tweets summarization is proposed in
[
        <xref ref-type="bibr" rid="ref23">22</xref>
        ] For including social aspects, Zhao et al. proposed to
do keyphrase extraction while they used an interestingness
score for capturing social attribute[
        <xref ref-type="bibr" rid="ref29">28</xref>
        ]. A multi-document
summarizer that takes into account social features is
proposed in [
        <xref ref-type="bibr" rid="ref18">17</xref>
        ]. Moreover, a lexical graph expansion for
extracting keyphrases through social hashtags is shown in [
        <xref ref-type="bibr" rid="ref3">2</xref>
        ].
      </p>
      <p>
        A number of graph-based keyphrase extraction approaches
have been proposed. TextRank[
        <xref ref-type="bibr" rid="ref21">20</xref>
        ], LexRank[
        <xref ref-type="bibr" rid="ref10">9</xref>
        ], NE-Rank[
        <xref ref-type="bibr" rid="ref4">3</xref>
        ],
SingleRank[
        <xref ref-type="bibr" rid="ref26">25</xref>
        ], and TopicRank[
        <xref ref-type="bibr" rid="ref1 ref6">5</xref>
        ]. These algorithms
leverage a random walk to calculate the centrality of either words
or sentences. For instance, NE-Rank considers node weights
being tf-idf of words and edge weight being freqancy of
cooccurrence of pairs of words. However, they all use simple
graphs not hypergraphs. In this paper, we consider a
highorder co-occurrence relation modeled in a hypergraph.
      </p>
      <p>
        Hypergraph random walks have been proposed in [
        <xref ref-type="bibr" rid="ref30">29</xref>
        ][
        <xref ref-type="bibr" rid="ref2">1</xref>
        ].
We further extend the aforementioned approaches in this
work to include vertex weights. Wang et al. proposed to
use a semi-supervised ranking approach based on Zhou et
al.[
        <xref ref-type="bibr" rid="ref30">29</xref>
        ] for ranking sentences which they used for text
summarization[
        <xref ref-type="bibr" rid="ref27">26</xref>
        ]. Li et al.[
        <xref ref-type="bibr" rid="ref15">14</xref>
        ][
        <xref ref-type="bibr" rid="ref16">15</xref>
        ] proposed a semi-supervised
(1)
(2)
(3)
      </p>
      <p>De and Dv are the diagonal matrices representing the
degrees of hyperedges and vertices, respectively. We is the
diagonal matrix with the hyperedge weights.
4.</p>
    </sec>
    <sec id="sec-5">
      <title>PROPOSED APPROACH</title>
      <p>The HG-Rank model captures keyphrases using a
hypergraph structure where it is possible to inherently model
social and temporal features. These features are embedded
as a hyperedge weight that represents a specific short
document. In essence, we model each short text document
di as a bag-of-words model with distinct keywords di =
{k1, k2, ..., ks}. A collection of documents Di = {d1, d2, ..., dn}
is then represented as a lexical hypergraph in the following
manner. We represent each short document as a hyperedge,
and each keyword as a distinct vertex.</p>
      <p>In this section, we will describe the HG-Rank algorithm
in more depth. First, the calculation and insertion of the
temporal and social attributes is going to be explained.
Second, the vertex weights will be explained. Third, we will
define the random walk ranking approach on the lexical
hypergraph to rank keywords. Finally, we will discuss our
approach on extracting keyphrases.
4.1</p>
    </sec>
    <sec id="sec-6">
      <title>Modeling Temporal &amp; Social Features</title>
      <p>
        Temporal attributes in a dynamic genre as a
microblogging social network or news trends is an important
dimension to understand evolving topics and keyphrases. We
measure the temporal effect as a ranking function for short
documents. The more recent the document, the higher the
temporal rank will be. Similar to [
        <xref ref-type="bibr" rid="ref28">27</xref>
        ][
        <xref ref-type="bibr" rid="ref25">24</xref>
        ], we measured the
temporal effect as the following:
      </p>
      <p>Rtime(di) = Q(c−yi)/24
(4)
Where c and yi denote the current time and the document
di publication time, respectively. (c − yi) is the time interval
between current and publication time in hours. We divide
by 24 to show the difference of publication time and current
time in number of days. Q is a decay rate parameter with
values 0 &lt; Q &lt; 1. Moreover, the Q value is inversely
proportional to favoring recent documents. When Q is closer to
0, the ranking favors very recent documents over old ones.
On the other hand, when Q is closer to 1, the ranking is less
focused on new documents. In our experiments, we set Q to
0.5.</p>
      <p>For the social effect, we measure the social dimension of
documents as a ranking function. The more popular or
shared the document, the higher the social rank will be. For
example in Twitter, tweets that are re-tweeted frequently
should be more important than a tweet without re-tweets.
This is similar to other social networks with the ”like”
feature as in Facebook or product reviews. We calculate the
social ranking as follows:</p>
      <p>Rsocial(di) =</p>
      <p>si + 1
Pe se + 1
(5)
Where si is the counter of social feature (counts of re-tweet
or likes) for document di. Pe se is the sum of all social
features across all documents (total number of re-tweets for
example). Moreover, we added one smoothing to avoid
canceling out documents with no social attributes.</p>
      <p>Now we tie both temporal and social features together in
one ranking function as follows:
w(di) = λRsocial(di) + (1 − λ)Rtime(di)
(6)
λ is a smoothing parameter with 0 &lt; λ &lt; 1 to trade off
the effect of temporal aspects and social aspects. We
experimented with different values for λ which will be discussed
in the experiment section. The final documents rank w(di)
will be embedded in the hypergraph as a hyperedge weight
to reflect documents’ importance over keywords. The
intuition behind embedding temporal and social features in
the ranking scheme is that they are essential for capturing
keyphrases in a dynamic genre. In a dynamic genre, as in
Twitter, the content rapidly changes with time. Hence, the
keyphrases tend to change as well. Conventional keyphrase
extraction algorithms do not consider the time dimension
in finding keyphrases which make them insufficient for the
task. Moreover, the social aspect is important to capture
keyphrases of trendy topics that social network users find
interesting. An interesting topic in social media will more
likely be searched compared to other topics which makes
it important to find its keyphrases. We will discuss vertex
weights in the next section.
4.2</p>
    </sec>
    <sec id="sec-7">
      <title>Modeling Discriminative Weights as Vertex Weights</title>
      <p>Graph-based approaches base the ranking on the
relational structure of co-occurring words. Such ranking is great
on capturing the semantic relation between words. However,
there is no evidence that graph-based ranking approaches
are able to capture discriminative words. To enhance the
hypergraph-based ranking algorithm, we use a
discriminative weighting scheme tf-idf as vertex weights before we start
the random walk. This injection of tf-idf weights will add
a discriminative perspective for calculating the rank though
a random walk approach. However, when applied to short
text documents, tf-idf fails to capture descriptive terms due
to sparsity of features (short length). To circumvent the
sparsity problem, we aggregate short documents to a
virtual larger ones and then calculate tf-idf scores. A larger
virtual document δ is the concatenation of smaller
documents d which is δt = {d1 + d2 + ... + dn}. In Section 5.3,
different approaches for aggregation are described in more
depth. We measure the normalized tf-idf over the larger
documents being the set of D = {δ1, δ2, ..., δn}. The tf-idf is
measured as follows:
w(vi)tf-idf =
tf (vi)</p>
      <p>Nw
· log</p>
      <p>N
df (vi)
(7)
Where tf (vi) as the term frequency on the document δ and
Nw is sum of all words occurrences in document δ for
normalization. N is the number of documents in the larger
document set D, and df (vi) is the number of larger
documents in D that contain the term vi. We will discuss the
hypergraph ranking algorithm HG-Rank in detail in the
next section.
4.3</p>
    </sec>
    <sec id="sec-8">
      <title>HG-RANK: Ranking in a Hypergraph</title>
      <p>To rank vertices in a hypergraph, we generalize a random
walk process for hypergraphs. A random walk process is the
transitioning between vertices in a graph by starting at a
given vertex and moving to another neighboring vertex
after each discrete time step t. We can imagine vertices as a set
of states {s1, s2, ..., sn} and the transitioning to be a finite
Markov chain M over these states. The transition
probability calculated as P (u, v) = P rob(st+1 = v|st = u) which
means that the chain M will be at v at time t + 1 given that
it was observed at u at time t. The Markov chain herein
is homogeneous which means that the transition
probability is independent of time t. Note that for any vertex u we
have Pv P (u, v) = 1. Since M is homogeneous with
probabilities computed over only a single transition, we can then
define a transition matrix P ∈ R|V |×|V | for all moves. The
transition matrix P captures the transition between vertices
which shows the behavior of a surfer randomly moving
between vertices according to such probabilities. Next we will
show how we define the random walk in hypergraphs.</p>
      <p>In simple graphs2, the random walk process is clear by
simply choosing an edge with a probability to a destination
vertex. However, it is not the case in hypergraphs where the
structure of the graph is substantially different demanding a
more general walk. For instance, in a hypergraph, a
hyperedge could have more than two end-point vertices δ(e) ≥ 2.
To generalize the random walk process in hypergraphs, we
model the walk as the transition between two vertices that
are incident to each other in a hyperedge instead of a normal
edge. In essence, the random walk is seen to be a two-step
process, instead of one, which is the following: the random
surfer first chooses a hyperedge e incident with the current
vertex u. Then the surfer picks a destination vertex v within
the chosen hyperedge satisfying the following u, v ∈ e. The
2By simple graphs, we mean graphs (not hypergraphs) with
edges that are unique pair of vertices. Not to be confused
with simple vs. multigraph
random walk in hypergraph is said to be more general since
the random walk in a normal graph is a special case where
there is only a single destination vertex v associated with a
given normal edge incident with u where in a hypergraph we
can have more vertices to choose from. The hypergraph
random walk process can be defined as a Markov chain where
the vertex set is the state set of the chain similar to a normal
graph. At each time step t the surfer moves in the incident
hyperedge to another vertex.</p>
      <p>In this paper, we try to seek a general definition of a
random walk in a weighted hypergraph where not only
hyperedges have weights, but vertices as well. In such a case, the
random walk process is extended to leverage both
hyperedges’ and vertices’ weights. We define the vertex’s weight
across all incident hyperedges to be a feature vector
~vw = {w(ve1), w(ve2), ..., w(vd(v))}
(8)
Where we have a different vertex’s weight for every
hyperedge e that contain vertex v. We describe the proposed
random walk process as the following. Starting from a vertex
u, the surfer chooses a hyperedge e incident with u
proportional to the hyperedge weight w(e). Then, the surfer, also
chooses a vertex v proportional to the vertex weight within
the hyperedge where we consider the weight in the current
hyperedge only. Let us define a weighted hypergraph
incident matrix Hw ∈ R|V |×|E| where we have the following:
hw(v, e) =
(w(ve) if v ∈ e
0</p>
      <p>if v ∈/ e
δ(ew) =</p>
      <p>X hw(v, e)
v∈V</p>
      <p>Therefore, we redefine the hyperedge degree to be as
follows:
(9)
(10)
(11)
We can now calculate the transition matrix P as follows:
P (u, v) =
e∈E
X w(e) P
h(u, e)</p>
      <p>hw(v, e)
eˆ∈E(u) w(eˆ) Pvˆ∈e hw(vˆ, e)
Or in matrix notation:</p>
      <p>P = Dv−1HWeDv−e1HwT</p>
      <p>Where hw(v, e) is the weight of the destination vertex v
in hyperedge e. Dv is the diagonal matrix of the weighted
degree of vertices as in formula 2. We is the diagonal matrix
of the hyperedge weights. Dve is the diagonal matrix for
weighted degree of hyperedges as in formula 10. Note that
the transition matrix P is stochastic where we have every
row sums to 1.</p>
      <p>After calculating the transition matrix P , we now explain
the stationary distribution π of a random walk. The
stationary distribution can be calculated by starting with initial
column vector ~v0 ∈ R|V |×1 with equal probabilities 1/|V |
summing to 1. We first multiply the transition matrix P T (where
P T is a column stochastic matrix for clarity) by the initial
column vector ~v0 yielding ~v1 = P T ~v0. Then, we iterate until
the vector ~v stops changing. The reason of multiplying the
probability distribution vector ~v by the transition matrix
P T gives us the next step distribution ~x = P T ~v can be
explained as follows. Let xi be the probability of being at the
current vertex i. Then we have the following: xi = Pj pij vj
where vj being the probability of the surfer being at node j
previously, and pij is the probability of moving from j to i.</p>
      <p>
        The probability distribution vector ~v stops changing after
n steps if the random walk is ergodic. A random walk is
ergodic when the following conditions are met: 1) the chain
is irreducible, for any two states si, sj ∈ M they must
satisfy P (si, sj ) &gt; 0. Also, 2) the chain is aperiodic, where the
greatest common divisor of every state {t : Pt(si, si) &gt; 0}
is 1. To guarantee irreducibility and aperiodicity, we use
the PageRank algorithm [
        <xref ref-type="bibr" rid="ref7">6</xref>
        ]. The algorithm uses the idea of
teleporting which will restart the random walk process
making it useful for the previous conditions. The teleporting is
depicted with a small probability called the damping factor
α. It also makes sure to make the graph irreducible since
the random walker always has the probability of teleporting
to any other node.
      </p>
      <p>~v(i+1) = αP T ~v(i) + (1 − α)~e/n
(12)
The damping factor α is set to 0.85. n is the number of nodes
in the graph. ~e ∈ Rn×1 is a vector of all elements being
1. αP T ~v means that the random walker will choose to go
with one of the incident hyperedges. (1 − α)~e/n represents a
vector of an introductory probabilities with each entry being
(1 − α)/n to teleport the random walk to a new node.
4.4</p>
    </sec>
    <sec id="sec-9">
      <title>Extracting Keyphrases</title>
      <p>
        We tag keywords with their Part of Speech (POS) tags.
Then, we extract keyphrases that are noun phrases since it
has been shown that most keyphrases annotated by human
happen to be noun phrases[
        <xref ref-type="bibr" rid="ref13">12</xref>
        ][
        <xref ref-type="bibr" rid="ref19">18</xref>
        ][
        <xref ref-type="bibr" rid="ref26">25</xref>
        ]. We look for patterns
as adj+nouns or all nouns and filter out the rest. Then, we
have a candidate list of keyphrases based on the syntactic
filtering that need to be ranked. A keyphrase ph is modeled
as a collection of keywords k as ph = {k1, k2, ..., kn}. To
rank a keyphrase, most approaches aggregate the ranks of
the keywords as follows:
      </p>
      <p>R(ph) = X R(ki)
ki∈ph
(13)
However, such approach will be biased towards longer phrases.
To overcome such bias, we normalized based on the length
of the keyphrase as follows:</p>
      <p>R(ph) = Pki∈ph R(ki) (14)
n
Where n is the keyphrase length. Moreover, we removed
phrases that cross over syntactic boundaries as they
cannot be a comprehensible keyphrase. We also removed any
keyphrase that appears less than f times. We experimented
with different values of f and found out that f = 5 shows
the best keyphrases in our data. Next we will describe the
experimental design in depth and all comparisons.
5.</p>
    </sec>
    <sec id="sec-10">
      <title>EXPERIMENT</title>
      <p>This section explains the experimental setup for the
hypergraph ranking framework HG-Rank. The effectiveness
of our approach is demonstrated by conducting several
experiments comparing our method to different baselines. First,
the data sets used in this experiment are explained
thoroughly. Second, the necessary preprocessing steps are
illustrated in detail. Third, the experimental setup is laid out.
Fourth, the experimental results and discussion of results
are discussed and examined.
5.1</p>
    </sec>
    <sec id="sec-11">
      <title>Data Sets</title>
      <p>
        We used two different data sets that contain only short
text documents. The characteristics of the two data sets are
explained as the following:
• Twitter. We collected a corpus of tweets which
contains 80,231 tweet posts. We collected tweets in the
time frame from April 1, 2013 to April 30, 2013. We
filter out all non-Latin characters tweets. Afterwards, we
deleted any non-English tweets by classifying a tweet
to be non-English if there is less than 5 English words.
Moreover, we discarded any tweet with less than 3
words as it does not show any topic relevance.
Moreover, the corpus contains 19,613 hashtags in total.
• Opinosis. We used a public short reviews data set
called Opinosis3 collected by Ganesan et al.[
        <xref ref-type="bibr" rid="ref11">10</xref>
        ]. The
data set contains short reviews, a sentence long, about
products collected from TripAdvisor, Amazon, and
Edmunds. The data set contains 51 topics about a
number of different products. For each topic, there is
approximately a 100 short review snippet. A golden
summary for each topic is created to summarize the
reviews. There are 5 different golden summaries for each
topic created by human workers from Amazon
Mechanical Turk (MTurk)4. We randomly used 3 different
topics to quantitatively test our algorithm with other
baselines which are Windows7 features, iPod video,
and Amazon’s kindle price.
5.2
      </p>
    </sec>
    <sec id="sec-12">
      <title>Preprocessing</title>
      <p>
        Preprocessing is an essential step in text mining tasks
in general. In extracting keyphrases, the preprocessing is
needed to measure the salient scores accurately. The amount
of preprocessing differs significantly depending on the genre
of the corpus. In a social microblogging environment as
in Twitter, the preprocessing step is of a vital importance.
The challenge with colloquial textual content is an enormous
obstacle in performing keyphrase extraction with Twitter
posts. For instance, tweets can have misspelled words, strange
capitalization, and wrong punctuations. For more detail we
refer the reader to Eisenstein’s survey on languages in social
media [
        <xref ref-type="bibr" rid="ref9">8</xref>
        ]. Therefore, we did in an extensive preprocessing
to tweets.
      </p>
      <p>We first removed any URL links from tweets since we are
focusing on the textual content. Moreover, we also removed
emoticons and smileys since they do not have any topical
relevance. Also, Twitter’s special characters and usernames
were removed as in the preceding hashtag sign # and
usernames with @username. Tweets that start with the
@username are generally considered replies and have a
conversational nature more than topical nature. Therefore, we have
removed any tweet that starts with @username to focus on
topical tweets only. Another challenge is the usage of
Internet phrasal abbreviation such as LOL (laugh out loud), ikr
(I know right). We leverage the Internet Slang5 dictionary in
an effort to transform the text to standard English. All the
aforementioned techniques can help improve the accuracy of
the POS tagger.
3http://kavita-ganesan.com/opinosis-opinion-dataset
4www.mturk.com
5http://www.noslang.com/dictionary/full/</p>
      <p>
        Syntactical tagging, as in POS, for conversational content
found on tweets can be very difficult. Most standard
taggers fail to correctly tag colloquial text. For instance, the
misuse of capitalization can make the tagger incorrectly tag
nouns or verbs as a proper noun simply because the token
is out of the vocabulary OOV. To tackle such difficulties,
we have leveraged a state-of-the-art POS tagger6 designed
specifically for tweets [
        <xref ref-type="bibr" rid="ref22">21</xref>
        ]. The tagger designed at Carnegie
Melon University is capable of accurately tagging tokens in
a noisy genre as in Twitter. Moreover, the tagger is capable
of identifying tags regardless of the capitalization misuse or
the strange orthography of text, for example repeating
letters for emphasis as in soooo. After tagging the tweets,
we focused on selecting nouns and adjectives only since they
are the base for noun phrases. We finally removed stopwords
and stemmed the tokens.
      </p>
      <p>The final step of preprocessing was to remove all
stopwords from tweets since they do not have any topical
influence. Punctuations were removed as well. Moreover, all
capitalized tokens were converted to lower case. We lastly
stemmed the tokens to get an accurate feature measure of
words. We used the Porter stemmer7 to stem our corpus.</p>
      <p>For the Opinosis data set, we removed stopwords,
punctuations, and stemmed the text. We also convert the tokens
to lower case.
5.3</p>
    </sec>
    <sec id="sec-13">
      <title>Experimental Setup</title>
      <p>In this section, we will describe the experimental setup
that was used for both data sets to compare our model with
other baselines. First, we will describe the setup used for
the Twitter data set. Then, we will explain the setup for
the Opinosis review data.</p>
      <p>
        Since there is no apparent golden labels to test against
with tweets, we designed an empirical experiment to test
keyphrase extraction in tweets. The experiment can be
designed into different steps 1) Identify major topics in
documents (tweets). 2) Test if any top ranked phrase represents
a major topic in documents. The intuition behind the
approach is the fact that phrases are descriptive of a document
if they explain an important topic within that document.
Given that keyphrases describe the major topics in a
document, we will leverage a statistical topic model known as
latent Dirichlet allocation (LDA)[
        <xref ref-type="bibr" rid="ref5">4</xref>
        ] to first extract the main
topics in documents using a new twitter representation that
improves the topic model with short documents. Second, we
use search engines to search these topics to generate
goldlabel phrases. Finally, we test and compare all the ranking
baselines by using the search results from the major topics
in Twitter and golden summaries in Opinosis separately.
      </p>
      <p>LDA is a generative statistical model that helps
finding a set of unobserved groups using some observed sets.
When applied to text, the observed sets are words in
documents where the unobserved groups (latent) are topics of
co-occurring words. By finding the mixture of topics using
statistical inference as in Gibbes sampling, we get two
posterior distribution P (w|k) the probability of words under each
topic, and P (k|d) the probability of topics under each
document. We first start by assigning each word to a K topic.
Then, for each word w in each document d, we resample the
6http://www.ark.cs.cmu.edu/TweetNLP/
7http://tartarus.org/martin/PorterStemmer/
● LDA Agg</p>
      <p>Normal LDA
●
5
●
6</p>
      <p>
        Number of Topics
Where P (wi|ks) is the probability of the word wi being
assigned topic ks from all documents. P (ks|d) is the
probability of words in the document d that are assigned to topic
ks. However, when applied to short length documents as
in tweets, a new challenge arises since there is not enough
observed sets (words) in each document to infer latent
topics. Therefore, we remodel the documents structure to
improve LDA in our data and get meaningful topics. Given
a collection of tweets Ti = {τ1, τ2, ..., τn}, there is an
abundant number of hashtags Hi = {h1, h2, ..., hn} appearing in
tweets. Instead of treating each tweet as a document, we
aggregate tweets using hashtags to form a large virtual
document for each hashtag dh = {τ1h+τ2h+...+τnh} where each
dh is a concatenation of tweets. Therefore, the documents
set will be defined as Dh = {dh1, dh2, ..., dhn} containing all
words from a large group of tweets for each document. After
enhancing the document representation, we can apply LDA
to learn topics and their posterior ranking more efficiently.
In Figure 1, we show a significant improvement in perplexity
for the two LDA approaches with short documents and
aggregated documents. In Table 1, we show the top 10 ranked
word for |K| = 5. Similar approaches for improving LDA in
short text documents are found in [
        <xref ref-type="bibr" rid="ref20">19</xref>
        ].
      </p>
      <p>To test the hypergraph ranking, we would need to have
a reference set that summarize topics within each dh
document. The idea is to use a search engine by using the top
words, from LDA, for each topic as a query. We used Google
to generate the result snippets by setting the search at the
same duration as the tweets which is April, 2013. Once the
search snippets (top 50 snippet) for each topic is collected,
we store them. Then we assign each document to its
major topics only. For instance, any topic that is higher than
P (k|d) = 0.5 is considered a major topic and is then
chosen. Those search results collected from the major topics
are considered references. We, then, search for keyphrases
in those topical references. If a keyphrase is included in a
snippet of any major topic, we consider it a hit, otherwise
it is a miss.</p>
      <p>For the Opinosis review data, we compared the extracted
keyphrases from short review documents with the golden
summaries provided with the data set. We consider a keyphrase
correct if it appears in any short golden summary. There is
approximately 5 golden summaries for each topic. Due to
the short length of documents, we only used bigrams for
evaluation.</p>
      <p>
        A number of different baseline algorithms are implemented
and used to test the validity of the proposed approach:
• tf-idf each post is a document, and each topic
collection is a reference corpus.
• TextRank[
        <xref ref-type="bibr" rid="ref21">20</xref>
        ] builds a graph of keywords with sliding
window w = 2. Edge weights are the frequency of
cooccurring relation.
• TimedTextRank[
        <xref ref-type="bibr" rid="ref25">24</xref>
        ] builds a graph of keywords
similar to TextRank. The ranking is, however, multiplied
by a time function over the destination node.
• NGTS(normal graph with Time and Social) A
normal lexical graph similar to TextRank. However,
the edge weights are the summation of temporal and
social function over all documents that contain the
pair of words u and v (instead of frequency of
cooccurrence)
• NE-Rank[
        <xref ref-type="bibr" rid="ref4">3</xref>
        ] A normal lexical graph similar to
TextRank. However, the ranking takes into account node
and edge weights. Node weights are tf-idf and edge
weights are the frequency of co-occurrence. It also
considers node weights when the random walk teleports to
a random node.
5.4
      </p>
    </sec>
    <sec id="sec-14">
      <title>Experimental Results &amp; Discussion</title>
      <p>To compare all the baselines used in this experiment, we
quantitatively measure their performance using a precision
evaluation metric. We compare them to the golden labels
defined in the previous section. Specifically, we consider the
keyphrase to be correct if it appears in the golden set.
Precision helps identify the accuracy of the extracted results.
Since we are evaluating a ranking system, we measure
precision at the top 10, 15, and 20 ranked keyphrases. Precision
is measured as follows:</p>
      <p>P recision =</p>
      <sec id="sec-14-1">
        <title>Kcorrect</title>
      </sec>
      <sec id="sec-14-2">
        <title>Kextracted</title>
        <p>(16)
Social and Temporal Parameter
●
20
●
25
Where Kcorrect is the number of correctly extracted keyphrase,
and Kextracted is the total number of extracted keyphrase.
In the following, we will discuss the experimental results
with balancing social and temporal attributes and how it
affect the ranking. Then, we will describe the improvements
HG-Rank has over other approaches.</p>
        <p>
          However, precision only considers how many correctly
extracted keyphrases within the result regardless of the
order within the top list of extracted keyphrases. Therefore,
we also measure the Binary Preference Measure Bpref [
          <xref ref-type="bibr" rid="ref8">7</xref>
          ].
Bpref will penalize the system if incorrect keyphrases ranked
higher than correct keyphrases. Bpref is measured as the
following:
        </p>
        <p>r∈R
Bpref = 1 X 1 − |n ranked higher than r|</p>
        <p>R R
(17)
where R is the number of correct keywords within
extracted keywords in a method, and where r is a correct
keyword and n is incorrect keyword.</p>
        <p>To examine the effect of social and temporal attributes
when combined into the hypergraph ranking scheme, we
experimented with different values for λ in formula 6. By
varying the value of λ, we can analyze the tradeoff between
the two attributes in precision. Figure 2 shows the
different λ values experimented with. The best value for λ is 0.5
which means equal contribution of temporal and social
features in our data. It is interesting to notice that when λ = 1,
meaning only social attributes were taken into the ranking,
the performance deteriorates considerably. It could mean
that popular content is not necessary of a topical value to
the corpus. However, more experiments are needed to widen
our understanding of what the best features are for topical
keyphrase extraction in a dynamic genre as Twitter. Next,
we move on to describe the full evaluation of both data sets.</p>
        <p>To evaluate the ranking performance for all baselines, we
performed the evaluation measure for both data sets as the
following. For Twitter, we first build the lexical hypergraph
for each hashtag topic corpus dh = {τ1h + τ2h + ... + τnh}.
We chose the top 5 frequent topical hashtags and performed
keyphrase extraction separately. We measured the precision
and Bpref for each topic. In table 2, we show the average
precision from all topics. Table 4 shows the average Bpref for
the Twitter data. In the Opinosis review data set, we build
.10 ● λ = 0</p>
        <p>λ = 0.5
● λλ == 10.8
the lexical hypergraph for each topic. Since there is no meta
data with the reviews as time or social features, we regard
the hyperedge weight to be 1 for all short documents to test
the hypergraph ranking only. We chose 3 topics mentioned
early to quantitatively measure the improvements. We show
the average precision of three topics in table 3, and average
Bpref in table 5.</p>
        <p>
          In the Twitter data, the proposed hypergraph-based
approach HG-Rank out performed all other baselines.
Specifically, HG-Rank improved the results in the top 10 results
over closest baseline, NE-Rank, by 14% and 7%
improvements using precision and Bpref, respectively. The
improvement shows the importance of modeling the high-order
cooccurring relationship using a lexical hypergraph compared
to modeling just a pair of words for graph edges. Moreover,
the temporally-aware ranking HG-Rank showed
improvement over other temporal-aware approaches as in
TimedTextRank[
          <xref ref-type="bibr" rid="ref25">24</xref>
          ] and NGTS. Similar improvements are
demonstrated for the top 15 and top 20 keyphrases.
        </p>
        <p>For the Opinosis data, HG-Rank showed improvement
over all baselines as well. Improvements in the top 10 over
the second best baseline, NE-Rank, were 10% in precision
and 14% in Bpref. Moreover, similar improvements were
found in the top 15 and top 20 keyphrases. Even though no
hyperedge weights were used for this data set as in temporal
and social attributes, the hypergraph model has shown to
increase both precision and Bpref scores which shows the
robustness of the proposed model in modeling high-order
co-occurrence relation between words.</p>
      </sec>
    </sec>
    <sec id="sec-15">
      <title>6. CONCLUSION</title>
      <p>In this paper, we have proposed a hypergraph-based
ranking algorithm suitable for short text documents in social
media genre. We modeled distinct keywords as vertices
and their short documents as hyperedges in a lexical
hypergraph. Moreover, we jointly modeled temporal and social
features in the hypergraph to adapt keyphrase extraction
with the dynamic nature of social media. Additionally, we
supplemented the hypergraph with discriminative weights
in the vertices to enhance the random walk approach. Then
we proposed a new probabilistic random walk that
considers both vertices and hyperedges weights over hypergraph.
We have leveraged a state-of-the-art POS tagger for
Twitter data to capture syntactic tags accurately from the noisy
text. We demonstrated the effectiveness of our hypergraph
approach over two data sets which showed promising results.</p>
      <p>In the future work, we plan to extend the approach to a
streaming algorithm where the hypergraph can be updated
periodically.</p>
    </sec>
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