Topic Detection by Clustering Keywords
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Topic Detection by Clustering Keywords
Conference Paper · October 2008
DOI: 10.1109/DEXA.2008.120 · Source: IEEE Xplore
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Topic Detection by Clustering Keywords
Christian Wartena and Rogier Brussee
Telematica Instituut, P.O. Box 589, 7500 AN Enschede, The Netherlands
{Christian.Wartena,Rogier.Brussee}@telin.nl
Abstract
We consider topic detection without any prior knowledge
of category structure or possible categories. Keywords are
extracted and clustered based on different similarity mea-
sures using the induced k-bisecting clustering algorithm.
Evaluation on Wikipedia articles shows that clusters of key-
words correlate strongly with the Wikipedia categories of
the articles. In addition, we find that a distance measure
based on the Jensen-Shannon divergence of probability dis-
tributions outperforms the cosine similarity. In particular,
a newly proposed term distribution taking co-occurrence of
terms into account gives best results.
1. Introduction
In this paper we consider the problem of finding the
set of most prominent topics in a collection of documents.
Since we will not start with a given list of topics, we treat
the problem of identifying and characterizing a topic as an
integral part of the task. As a consequence, we cannot rely
on a training set or other forms of external knowledge, but
have to get by with the information contained in the col-
lection itself. The approach we will follow consists of two
steps. First we extract a list of the most informative key-
words. Subsequently we try to identify clusters of keywords
for which we will define a center, which we take as the rep-
resentation of a topic. We found that this works fairly well
in an evaluation with Wikipedia articles in which we com-
pared human defined topic categories with keyword clus-
ters.
Clustering of (key)words requires a similarity or distance
measure between words. In this paper we consider distance
measures between words that are based on the statistical dis-
tribution of words in a corpus of texts. The focus of is to find
a measure that yields good clustering results.
The organization of this paper is as follows. In section
2 we discuss related work and the related problem of key-
word extraction. In section 3 we discuss distance functions
and introduce different probability distributions needed to
define them. We end the section with a brief description
of the clustering algorithm used for evaluation. Finally, in
section 4 we present an evaluation of topic detection on a
Wikipedia corpus using clustering of keywords with differ-
ent distance measures.
2. Related Work
Much work has been done on automatic text categoriza-
tion. Most of this work is concerned with the assignment
of texts onto a (small) set of given categories. In many
cases some form of machine learning is used to train an
algorithm on a set of manually categorized documents. A
lot of work has been done on clustering of texts (See e.g.
[14] and [12]) which has already found practical applica-
tions like the clustering of search results (see e.g. http:
//clusty.com/).
The topic of the clusters remains usually implicit in these
approaches, though it would of course be possible to apply
any keyword extraction algorithm to the resulting clusters
in order to find characteristic terms.
Like the work presented in this paper, Li and Yaman-
ishi ([10, 9]) try to find characterizations of topics directly
by clustering keywords using a statistical similarity mea-
sure. While very similar in spirit, their similarity measure
is slightly different from the Jensen-Shannon based similar-
ity measure we use. Moreover, they focus on determining
the boundaries and the topic of short paragraphs, while we
try to find the predominant overall topic of a whole text.
Both our and their work are conceptually related to latent
semantic analysis (LSA) [3, 7] and even more so to proba-
bilistic latent semantic analysis (PLSA) [5, 6] and related
work by [15]. The input for both our methods and (P)LSA
is the word occurrence and co-occurrence data of terms.
Latent semantic analysis now naturally leads to weighted
sums of terms, with the crucial difference that in the PLSA
case only non negative weights with sum 1 are allowed
which have a natural interpretation as conditional probabil-
ities. In the latent semantic analysis approach the analogue
of clustering is finding (latent) conditional probability dis-
tributions such that we can decompose the observed word
http://clusty.com/
http://clusty.com/
distributions into a few of these latent distributions and a
small “noisy” remainder. In this decomposition words with
strong mutual co-occurrence tend to have the same main la-
tent components. In our work the word clusters are similarly
based on co-occurrence data. This is achieved by comparing
and clustering distributions of co-occurring terms. Thus,
the center of a cluster is the average distribution of the co-
occurrence distributions, and is in this sense comparable to
a latent component.
3. Clustering Keywords
By clustering we will understand grouping terms, docu-
ments or other items together based on some criterion for
similarity. We will always define similarity using a distance
function on terms, which is in turn defined as a distance
between distributions associated to (key)words by counting
(co)occurrences in documents.
3.1. Keyword Extraction
We will represent a topic by a cluster of keywords. We
therefore need a set of keywords for the corpus under con-
sideration. Note that finding a set of keywords for a corpus
is not the same problem as assigning keywords to a text
from a list of keywords, nor that of finding the most char-
acteristic terms for a given subset of the corpus. The prob-
lem of finding a good set of keywords is similar to that of
determining term weights for indexing documents, and not
the main focus of this paper. For our purposes usable re-
sults can be obtained by selecting the most frequent nouns,
verbs (without auxiliaries) and proper names and filtering
out words with little discriminative power (see section 4).
3.2. Distributions
We simplify a document to a bag of words, terms or key-
words, in the following always called terms. We consider a
collection of n term occurrences W . Each term occurrence
is an instance of exactly one term t in T = {t1, . . . tm},
and can be found in exactly one source document d in a
collection C = {d1, . . . dM}. Let n(d, t) be the number of
occurrences of term t in d, n(t) =
∑
d n(d, t) be the num-
ber of occurrences of term t, and N(d) =
∑
t n(d, t) the
number of term occurrences in d.
We consider the natural probability distributions Q on
C × T , a distribution Q on C and q on T that measure the
probability to randomly select an occurrence of a term, from
a source document or both
Q(d, t) = n(d, t)/n on C × T
Q(d) = N(d)/n on C
q(t) = n(t)/n on T
These distributions are the baseline probability distributions
for everything that we will do in the remainder. In addition
we have two important conditional probabilities
Q(d|t) = Qt(d) = n(d, t)/n(t) on C
q(t|d) = qd(t) = n(d, t)/N(d) on T
The suggestive notation Q(d|t) is used for the source distri-
bution of t as it is the probability that a randomly selected
occurrence of term t has source d. Similarly, q(t|d), the
term distribution of d is the probability that a randomly se-
lected term occurrence from document d is an instance of
term t. Various other probability distributions on C × T ,
C and T that we will consider will be denoted by P, P , p
respectively, dressed with various sub and superscripts.
Distributions of Co-occurring Terms
The setup in the previous section allows us to set up a
Markov chain on the set of documents and terms which will
allow us to propagate probability distributions from terms
to document and vice versa. Consider a Markov chain on
T ∪C having transitions C → T with transition probabilities
Q(d|t) and transitions T → C with transition probabilities
q(t|d) only.
Given a term distribution p(t) we compute the one step
Markov chain evolution. This gives us a document distri-
bution Pp(d), the probability to find a term occurrence in a
particular document given that the term distribution of the
occurrences is p
Pp(d) =
∑
t
Q(d|t)p(t).
Likewise given a document distribution P (d), the one step
Markov chain evolution is the term distribution
pP (t) =
∑
d
q(t|d)P (d).
Since P (d) gives the probability to find a term occurrence
in document d, pP is the P-weighted average of the term
distributions in the documents. Combining these, i.e. run-
ning the Markov chain twice, every term distribution gives
rise to a new distribution
p̄(t) = pPp(t) =
∑
d
q(t|d)Pp(d) =
∑
t′,d
q(t|d)Q(d|t′)p(t′)
In particular starting from the degenerate “known to be z”
term distribution
pz(t) = p(t|z) =
{
1 if t = z ,
0 otherwise.
,
the distribution of co-occurring terms p̄z then is
p̄z(t) =
∑
d,t′
q(t|d)Q(d|t′)pz(t′) =
∑
d
q(t|d)Q(d|z).
This distribution is the weighted average of the term distri-
butions of documents containing z where the weight is the
probability Q(d|z) that a term occurrence in d is an occur-
rence of z.
Note that the probability measure p̄z is very similar to
the setup in [10, section 3]. The difference is that we keep
track of the density of a keyword in a document rather than
just the mere occurrence or non occurrence of a keyword in
a document. This difference is particularly relevant for long
documents where a word may occur with very low density,
yet because it contains many words have a significant con-
tribution to the mean word distribution. Unfortunately p̄z is
expensive to compute.
3.3. Distance Measures
An effective way to define “similarity” between two ele-
ments is through a metric d(i, j) between the elements i, j
satisfying the usual axioms of nonnegativity, identity of in-
discernables and triangle inequality. Two elements are more
similar if they are closer. For this purpose any monotone in-
creasing function of a metric will suffice and we will call
such a function a distance function.
For clustering we use a hierarchical top-down method,
that requires that in each step the center of each cluster is
computed. Thus our choice of distance function is restricted
to distances defined on a space allowing us to compute a
center and distances between keywords and this center. In
particular we cannot use popular similarity measures like
the Jaccard coefficient.
In the following we will compare results with four dif-
ferent distance functions for keywords t and s: (a) the co-
sine similarity of the document distribution Qt and Qs con-
sidered as vectors on the document space, (b) the cosine
similarity of the vectors of tf.idf values of keywords, (c) the
Jensen-Shannon divergence between the document distri-
butions Qt and Qs and (d) the Jensen-Shannon divergence
between the term distributions, p̄t and p̄s.
The cosine similarity of two terms t and s is defined as
cos simtf (t, s) =
Σd∈CQt(d)Qs(d)√(∑
d∈C Q
2
t (d)
) (∑
d∈C Q
2
s(d)
) .
Since the arccos of this similarity function is a proper met-
ric, (1− cos)(arccos(cos sim(t, s))) = 1− cos sim(t, s) is
a distance function.
The Jensen-Shannon divergence or information radius
[11, 4] between two distributions p and q is defined as
JSD(p||q) =
1
2
D(p||m) +
1
2
D(q||m)
where m = 1/2(p+q) is the mean distribution and D(p||q)
is the relative entropy or Kullback-Leibler divergence be-
tween p and q which is defined by
D(p||q) =
n∑
i=1
pi log
(
pi
qi
)
.
Since the square root of the Jensen Shannon divergence is a
proper metric [4], we have two distances
JSD simdoc(t, s) = JSD(Qt, Qs)
and
JSD simterm(t, s) = JSD(p̄s, p̄t)
3.4. Clustering Method
We have used the induced bisecting k-means clustering
algorithm as described by [1], which is based on the stan-
dard bisecting k-means algorithm, see e.g. [14]. An infor-
mal description of the method is as follows. We start by
selecting two elements that have the largest distance, which
we use as the seeds for two clusters. Next all other items
are assigned to the cluster closest to one of the two seeds.
After all items have been assigned to a cluster, the centers of
both clusters are computed. Here we need a representation
of items that naturally allows to define a center which typi-
cally is not an item proper but a weighted sum of items. The
new centers serve as new seeds for finding two clusters and
the process is repeated until the two centers are converged
up to some predefined precision. We have now found two
clusters. If the diameter of a cluster is larger than a specified
threshold value, the whole procedure is applied recursively
to that cluster. The algorithm therefore finds a binary tree
of clusters.
We also experimented with agglomerative hierarchical
clustering, especially the single link algorithm. First results
suggested that this approach performed not as well as the k-
means algorithm, in line with similar findings by [14] and
[12]. Since our focus is to find an optimal distance measure
and not to find the best clustering algorithm, we did not
investigate the agglomerative methods in more detail.
4. Evaluation
4.1. Implementation
To test and compare the different strategies we have com-
piled a small corpus of Dutch Wikipedia articles consisting
of 758 documents. In the analysis phase, 118099 term oc-
currences, and 26373 unique terms were found. The arti-
cles were taken from 8 Wikipedia categories: spaceflight,
painting, architecture, trees, monocots, aviation, pop mu-
sic, charadriiformes. Categories were selected for subjec-
tive similarity, like spaceflight and aviation, and subjective
dissimilarity like pop music and monocots. Articles are
equally distributed over the categories, but articles in some
categories are significantly longer than in others. Moreover,
homogeneity and specifity of articles differs significantly
between categories.
To determine a set of relevant keywords we have selected
the most frequent content words and filtered out a number
of overly general terms. The latter was done by requiring
that a keyword has to be different enough from the back-
ground distribution q, as measured by the Kullback-Leibler
divergence. We used a cutoff D(p̄t||q) > 1 bit, that turned
out to give decent results.
Before extracting keywords we do some preprocessing
using the GATE–framework [2]. The main analysis steps
are: lemmatization, multiword lookup and named entity
recognition. Lemmatization and tagging is done using the
Treetagger [13]. Tagging allows us to distinguish content
words from function words. After lemmatization all in-
flected forms of verbs, nouns and adjectives are mapped
onto their lexical form, substantially reducing the variation
in the input data. For multiword lookup we used article
titles from the Dutch Wikipedia, since it is reasonable to as-
sume that each title represents a single concept. Finally,
some simple rules are applied to identify proper names.
While some of the components are language dependent, all
of the components are available for a number of languages
within the GATE–framework.
We selected the 160 most frequent keywords fulfilling
this criterion and clustered them with the induced bisecting
k-means algorithm from section 3.4 using different distance
measures.
4.2. Results
To evaluate the implemented topic detection methods,
we have compared the results with topics known to be
present in the collection. We benchmarked against the 8
selected Wikipedia topics of the collection. Of course, it
is conceivable that the collection has more topics that au-
tomatic methods might recognize as well. To define a ref-
erence clustering, we have clustered the 160 selected key-
words into a set of 9 categories C∗ = {c∗0, c∗1, · · · , c∗9}, one
for each Wikipedia category and a rest cluster c∗0, using the
following method. For each of the 8 Wikipedia categories
c∗i we compute the distribution qc∗i of words in the docu-
ments belonging to c∗i and we let qc∗0 = q. We assign a term
z to cluster c∗ if c∗ = argminc∗∈CD(qc∗ ||p̄z).
Following [8], we now compare with the set of clusters
C of keywords found using the algorithm in section 3.4,
different distance measures and different diameters. For
each cluster c ∈ C and cluster c∗ ∈ C∗ we define a re-
call measure rec(c, c∗) = |c∩ c∗|/|c∗|, a precision measure
prec(c, c∗) = |c ∩ c∗|/|c∗| and an F value
F (c, c∗) =
rec(c, c∗)prec(c, c∗)
1
2
(rec(c, c∗) + prec(c, c∗))
.
Let F (c∗) = maxc∈C F (c, c∗) be the F -value of the best
fitting found cluster and finally define the overall F-value
F =
∑
c∗∈C∗
|c∗|∑
c∗∈C∗ |c∗|
F (c∗)
A value of F = 1 therefore means that for each Wikipedia
and rest category the topic detection algorithm found a cor-
responding cluster.
Since the clustering algorithm can produce clusters of
different size, the quality of the result depends on the only
input parameter of the algorithm, the threshold value to split
up a cluster. Its quality (in terms of overall F-value) is com-
pared between distance functions by varying the number
of clusters as controlled by varying the threshold values.
Since there might be several clusters with exactly the same
largest distance between two elements, we do not find val-
ues for each number of clusters. In particular, for cos simtf
and JSD simdoc there are no values that yield a clustering
into less than 14 and 11 clusters, resp. In the case of co-
sine similarity there are in each of these clusters even two
keywords with completely orthogonal document distribu-
tions. The overall F-values for clustering with the different
similarities are given in Figure 1. Cosine similarity with
tf.idf vectors performed in between direct cosine similarity
and the Jensen-Shannon distance with the document distri-
bution
The rest category in the reference categorization is not a
real cluster or category of keywords. Moreover, this cate-
gory is about three times as large as the average size of the
other categories. We have therefore tested how well the 8
positively motivated categories are detected, and computed
the overall F-values averaging only over these 8 categories.
The results are given in Figure 2. Results for the cosine sim-
ilarity with tf.idf vector were slightly better than clustering
with JSD simdoc
5. Conclusions
The experimental results suggest that topic identification
by clustering a set of keywords works fairly well, using ei-
ther of the investigated similarity measures. In the present
experiment a recently proposed distribution of terms asso-
ciated with a keyword clearly gives best results, but compu-
tation of the distribution is relatively expensive. The reason
for this is the fact that co-occurrence of terms is (implicitly)
taken into account. The document distribution for terms,
Figure 1. Overall F-Measure for clustering
based on 9 categories
that is the base of the other measures, tend to be very sparse
vectors, since for a given document most words will not oc-
cur at all in that document. In the distribution used for the
JSD simdoc this problem alleviated by a kind of ’intelligent
smoothing’ or spreading values from one term to frequently
co-occurring terms.
Acknowledgements
This work is part of the MultimediaN project1 sponsored
by the Dutch government under contract BSIK 03031.
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https://www.researchgate.net/publication/4374762
. Introduction
. Related Work
. Clustering Keywords
. Keyword Extraction
. Distributions
. Distance Measures
. Clustering Method
. Evaluation
. Implementation
. Results
. Conclusions