Journal of Software Engineering and Applications, 2013, 6, 7-12
doi:10.4236/jsea.2013 .67B002 Published Online July 2013 (http://www.scirp.org/journal/jsea)
Clustering Student Discussion Messages on Online
Forumby Visualization and Non-Negative Matrix
Factorization
Xiaodi Huang1, Jianhua Zhao2, Jeff Ash1, Wei Lai3
1School of Computing and Mathematics, Charles Sturt University, Australia; 2Faculty of Education Information Technology, South
China Normal University, China; 3Faculty of Information and Communication Technologies Swinburne University of Technology,
Australia.
Received April, 2013
ABSTRACT
The use of online discussion forum can effectively engage students in their studies. As the number of messages posted
on the forum is increasing, it is more difficult for instructors to read and respond to th em in a prompt way. In this paper,
we apply non-negativ e matrix factorization and visualization to clustering message data, in order to provide a summary
view of messages that disclose their deep semantic relationships. In particular, the NMF is able to find the underlying
issues hidden in the messages about which most of the students are concerned. Visualization is employed to estimate the
initial number of clusters, showing the relation communities. The experiments and comparison on a real dataset have
been reported to demonstrate the effectiveness of the approaches.
Keywords: Online Forum; Cluster; Non-Negative Matrix Factorization; Visualization
1. Introduction
The online discussion forum has emerged as a common
tool that engages students in an effective way. As an
e-learning platform, it allows students to post messages
on a variety of issues to the various discussion threads.
The challenge, however, is that the number of online
forums and the number of messages posted on these fo-
rums are increasing. This is particularly true for distance
education in universities. For example, the first author’s
forum account in the university has 9016 messages dur-
ing the second semester of year 2012. It is impossible
and unnecessary to read all of these messages. How to
obtain a summary of these messages therefore becomes
particularly important.
From another perspective, student discussion messages
contain the rich information about students such as their
thinking and personality traits during the interactions. In
fact, interactivity is considered as a central tenet to the
concept of online learning theory [7]. Six types of inter-
actions namely student-student, student-instructor, stu-
dent-content, instructor-instructor, instructor-content and
content-content interactions are identified [7]. The mes-
sage data from an online discussion forum used in this
work are a student-issue matrix, where the issues include
the content. Based on this matrix, we reveal the hidden,
deep interaction relations of student-student, issue-issue,
and student-issue using cluster techniques.
In this work, we attempt to p rov ide a su mmary v iew of
messages on the forum by clustering the student-issue
interaction data. By means of clustering students and
issues, we are able to answer several questions below:
who is a group of representative students posting mes-
sage on the similar topics? what are the underlying topics
among issues posted on the forum? and what are the in-
terleaving relations between students and issues? Based
on answers to these questions, instructors can align their
pedagogies with students’ needs and take actions in a
timely manner.
For clustering students and issues, we use non-nega-
tive matrix factorization (NMF) [6] and visualize interac-
tion communities of students and issu es derived from the
message data. Effectively detecting the hidden underly-
ing topics, NMF has been successfully applied to clus-
tering different kinds of documents [5, 8, 9]. However, it
is difficult to specify the appropriate number of clusters.
We model the interactions among students and among
issues into two graphs, and then visualize them. Examin-
ing the graphs, we estimate the number of clusters, and
input it as the parameter of NMF. Although clusters
shown by the visualization are different from those de-
tected by NMF in terms of their underlying implications,

Clusterin g Student Discussion Messages on On line Forum by Visualiz a tion and Non-Negative Matrix Factorization 8
the estimation is still helpful for improving the perform-
ance of NMF in the experiments.
The contributions of this paper are as follows:
 We model the message data by graphs and visualize
them;
 We apply NMF to clustering the message data in the
student di sc ussion for um;
 We integrate the two approaches by estimating the
initial number of clusters from visualization.
The rest of this paper is organized as follows. Section
2 presents visualization of the relations among students
and issues. Related work is presented in Section 3. A
detailed description of the approach to clustering students
and issues is presented in Section 4, follo wed by an algo-
rithm for visualization and NMF in Section 5. Section 6
reports the experiment result s, and conclusion i n Section 7.
2. Related Work
The state-of-the–art of educational data mining can be
found in [12]. In particular, data mining approaches have
been applied to extract useful information from student
forum data [2, 3, 14]. They can simply be classified by
which types of approaches used and what kinds of in-
formation extracted. For the purpose of supporting online
learning management, facilitation, and design, Hung and
Zhang [13] apply data mining techniques to server logs,
in order to reveal the patterns of online learning behav-
iour. Lin, Hsieh, and Chuang [14] investigate the poten-
tials of an automatic genre classification system that can
facilitate the coding process of the content analysis of
data from a discussion forum. Agglomerative hierarchi-
cal cluster approach is applied to group the students with
the similar behaviour profiles that consist of their reading
and writing actions on an online discu ssion forum over a
time window [15].
Being applied to cluster different types of documents
[5,8,9], NMF has not yet been used to cluster the mes-
sages on an online forum. Our approach differs from
existing approaches in the different answers to two fun-
damental questions relating to clustering: what kinds of
features ar e used and how to specify the suitable number
of clusters. Instead of original features, students are clus-
tered by usingsemantic features that are derived from
grouping all semantically related discussion issues to-
gether.Our approach aims to discover parts-based repre-
sentations of the message data in a semantic space.Unlike
the visual analysis of online interaction patterns in [4],
graph visu alization in th is work is us ed for esti mating th e
number of clusters. We integrate visualization into NMF
in order to improve the performance.
3. Visualization of Students and Issues
In this section, we present the problem of clustering stu-
dents and their discussion issues on an online forum. It is
assumed that each message in the forum is associated
with two attributes: which issue (one issue) the message
is about and who (one student) posts. We also assume
that there is a set of m students and a set
of n issues{:1 }
i
Ss im
{:1 }
j
Tt jn

 . All message data in a fo-
rum during a given period can be represented as a stu-
dent-by-issue matrix mn
A


 where ij is a weight
assigned according to the number of messages on issue j
posted by user i. Equivalently, each row of matrix A
characterizes a student in terms of which and how many
issues she has posted. Each column represents an issue
described by which and how many students who have
posted messages on this particular issue. We can generate
an undirected graph G from the message data, namely G
= (V, E). For the student-student graph, we have V = S,
and build an edge between two nodes if
a


,0
ij
ssim s,
where

1
22
11
,(
n
il jl
l
ij nn
il jl
ll
aa
sim ssaa




1)
Similarly, we can generate the issue-issue graph.
According to Equation (1), we construct graphs that
illustrate the relations between the message data in the
forum and visualize them in Figure 1. As the densities of
the graphs in Figures 1(a) and (b) are high, it is difficult
to estimate the number of clusters. Therefore, we filter
the student-student graph into a simple one that can still
keep the important structural feature. Specifically, all
edges with the weights that are less than the specified
threshold are removed. For example, Figure 1(c) shows
the filtered graph of student-student with a weight
threshold of 0.997. In other words, the edges shown in
Figures 1(c) have weights that are not less than 0.997.
Examining this filtered graph, we estimate the number of
clusters to be 7 ~ 9. These numbers will be used as the
respective parameter of NMF in the experiments.
4. Cluster Students and Issues
In essence, clustering students and issues can be regarded
as compressing student-by-issue matrix A. In other words,
we use a compressed matrix to approximate the original
matrix of the message data. On the other hand, it is rea-
sonable to suppose that the issues raised in the message
from a forum are not completely independent of each
other. The issues may overlap in their topics involved. As
such, the axes of semantic space of the data that capture
each of the issues are not necessarily orthogonal. There-
fore, we use NMF to find the latent semantic structure of
the message data, and to identify clusters in the derived
latent semantic space.
It is assumed that the data can be grouped into k clus-
ters. Given a matrix A, the optimal choice is the

Clusterin g Student Discuss ion Messages on Online Forum by Visualiz ation and Non-N egative Matrix Factorization 9
(a)
(b)
(c)
Figure 1. Graph visualization on the relations of issue-issue
and student-student. (a) The issue-issue graph with 552
nodes and 5408 edges; (b)The student-student graph with
899 nodes and 8330 edges; (c)The student-student graph
with removing edges with weights being less than 0.997.
nonnegative matrices W and H that minimize the func-
tion of the reconstruction error betwee n A and WH:


22
,
,|| (())
Fij
ij
FWHA WHawh 
ij
(2)
where 1 () k
ijiji j
awh wh


 

 subject to the con-
straints of , and , where 00
i
w

0
j
h

im

,
0k


, and 0jn

.
The dimensions of the factorized matrices W and H are
mk

and kn

, respectively. The W basis vectors can
be thought of as the “building blocks” of the data. Each
element ij of matrix W is also the degree to which
student i belongs to cluster j. The coefficient vector H
describes how strongly eac h b uilding block is present.
w
Assume that a message data set is comprised of k
clusters, each of which corresponds to a student group (a
coherent topic). Each student (issue) in the set either
completely belongs to a particular group, or is more or
less related to several groups (topics). To accurately
cluster a given message dataset, it is ideal to project the
all messages into a k-dimensional semantic space in
which each axis corresponds to a particular topic. Each
student can be represented as a linear combination of the
k topics about which she is mainly concerned. Because it
is more natural to associate each student with an additive
rather than subtractive mixture of the underlying topics,
the linear combination coefficients should all take
non-negative values.
As a nonlinear optimization problem, this has been
proved to be NP-hard. As such, the most popular heuris-
tic solution to the objective function of NMF is to use the
multiplicative update rule: () (3)
()
() (4)
()
ij
ij ijTij
Tij
ij ijTij
AH
ww
WH H
AW
hh
HW W


where W and H are randomly initialized. Their values are
then updated using the expectation maximization algo-
rithm [6].
Determining the cluster label for each data point is as
simple as finding the axis with which the data point has
the largest projection value.
Note that the clusters shown by the visualization are
different from those detected by NMF. For example, an
issue cluster by visualization is based on the similarities
of issues characterized by the frequency and types of
issues of messages students post (original features).
Topic clusters by NMF capture the semantic topic rela-
tions among issues of messages (derived semantic fea-
tures).It is parts-based decomposition of messages.
5. Algorithm
The detail of NMF graph visualization is given below.

Clusterin g Student Discussion Messages on On line Forum by Visualiz a tion and Non-Negative Matrix Factorization 10
NMF with the graph visualization algorithm
Input: A student-issue matrix A, and the number of k
Output: k student and topic clusters
(1) //Visualization
calculate the similarities between students according
to Equation (1)
similarly, calculate the similarities between issues
generate similarity graphs of student-student and is-
sue-issue
apply a layout algorithm to layout the graphs [10, 11]
re-layout the filtered graph
(2) // Run the NMF
randomly initialize Wand H with values of
,[0,1wh]
while (neither converge nor reach the maximum
number of iterations) {
update the elements of W for , and
0im
0k

, according to Equation (3)
update the elements of V for 0,and jn
0k

 according to Equation (4)
}// end of while
determine the resulting cluster of each student in each
row of W according to argmax
ii
s
cw



determine the resulting cluster of each issue in each
column of H according to argm ax
j
j
tc w



The time complexities of layout and NMF
are , respectively.
2
(),and()Om Okm
6. Experiments
In this section, we report our experiments on clustering
students and issues by applying non-negative matrix fac-
torization.
6.1. Dataset
Our experiments use the forum data that were collected
from an online community for the students at University
of California [1]. The dataset includes 899 us ers and 522
issues.
In order to obtain an overview of the data, we illustrate
the variances of different dimensions in Figure 2. It is
observed that issue 107 has the largest variability with
variance of 57, followed by issue 82 (52.16), issue 117
(43, 22). 33 issues including issues 142-148, and158
have the least variance of 0.0011.
6.2. Results
With the estimated number of clusters by graph visuali-
zation, and experiments with the data, we chose eight
clusters as the parameter. Applying NMF to the message
dataset, we obtain its compressed approximation of a WH
matrix with eight transformed attributes that are regarded
as clusters. The matrix W is 89 with the eight 9 8
Figure 2. The variances of students (row) and issues (col-
umn) in the matrix of the dataset.
columns representing transformations of the attributes.
The eight rows of the matrix H of represent the
coefficients of the linear combinations of the 552 original
attributes that produce the transformed attributes in W. In
other words, they give the relative contributions of each
of the 552 attributes in the original dataset to the trans-
formed attributes in W. As illustrated in Figure 3, each
cluster consists mainly of the different numbers of
dominating issues. From Table 1, furthermore, Clusters
1, 3, 4, and 8 are formed by one significant issue, respec-
tively. Cluster 3 has issue 145 with the weight as high as
0.95, while issue 93 with weight 0.91 in Cluster 8. Each
significant issue in each cluster is the most important
topic for university students. This may relate to their
studies, interest and their campus lives. Clusters 5 and 6
contain one or two dominating issues, together with a
few less significant, but still important issues. Several
dominating issues contribute almost evenly to Clusters 2
and 7. This may imply that these issues have common
topics in which some of students are interested. Different
composition patterns of the clusters reflect the fact: al-
though the issues concerned by the students are diverse,
they are associated with several hidden, underlying rea-
sons that can summarize the topics of all messages. NMF
is able to disclose underlying reasons behind the mes-
sages that students posted. These may include students’
interests, the difficulties in their studies, their opinions on
big event happening in the campus, and so on.
8552
From another perspective, each issue contributes dif-
ferently to the resulting clusters. Issue 117 with 1.28 in-
puts the most, followed by issue 82 with 1.04, issues 107
and 13 with 1.0, issue 59 with 0.94, and issue 93 with
0.93. Also, 30 issues such as 142 ~148, 439, and 538
with zero coefficients do not influence the resulting clus-
ters at all. 69 issues such as 539, 461, 417, and 517 with
close zero coefficients influence the clusters trivially.

Clusterin g Student Discuss ion Messages on Online Forum by Visualiz ation and Non-N egative Matrix Factorization 11
Figure 3. Weights of all issues distributed over each cluster.
Table 1. Dominating issues in each of the eight clusters.
Cluster Issue-Weight # issue with 0
1 82,0.86;377,0.17;319,0.15;169,0.13;
103,0.13; 435,0.12: 290
2 289, 0.55; 208, 0.32;117,0.48; 185, 0.29 241
3 145, 0.95; 146 0.25;147, 0.11; 28
4 59, 0.87; 13,0.23; 48,0.19 308
5 46,0.69; 13,0.57; 62,0.22; 446,0.18;94,0.18 302
6 117,0.66;109,0.38,28,0.31;438,0.28 335
7 218,0.36;39,0.26;169,0.26;56,0.24 119
8 93,0.91;74,0.31;358,0.21;91,0.07;175,0.07 348
The resulting clusters also have underlying pedagogy
implications, reflecting different aspects of students, such
as personalization, personality traits, communities, as-
sessment and feedback, and reflective thinking.
6.3. Performance and Comparison
The performance is evaluated by comparing the cluster
label of each student (issue) with its corresponding label
produced from the k-means algorithm. Two metrics of
the accuracy (AC) and mutual information (MI) are used
to measure the clustering performance. Given student si
let sci and k sci be the cluster label by NMF and by
k-means, respectively. The AC is defined as
1(, )
m
ii
i
s
cksc
AC m


 (5)
where the delta function (,)
x
y

is 1 if
x
y, and 0
otherwise.



,
,
(, )
(, )()
ij
ij
ij
scSC kscKSCij
MISC KSC
psc ksc
psc kscpsc pksc

 (6)
Table 2. Comparisons of resulting clusters by NMF and
K-means: S (student) and I (issue).
AC MI
k S I Ave. S I Ave.
2 0.90 0.45 0.62 1.91e-04 0.01 0.01
3 0.46 0.26 0.36 0.01 0.04 0.02
4 0.32 0.23 0.27 0.03 0.07 0.05
5 0.33 0.18 0.26 0.04 0.09 0.07
6 0.30 0.23 0.26 0.08 0.14 0.11
7 0.36 0.29 0.32 0.08 0.17 0.13
8 0.47 0.29 0.38 0.12 0.24 0.18
9 0.28 0.18 0.23 0.13 0.16 0.15
10 0.07 0.03 0.05 0.14 0.20 0.17
50 0.05 0.06 0.06 0.81 1.29 1.05
Ave. 0.35 0.22 0.28 0.14 0.24 0.19
where


,()
i
pscpksc
(, )
ij
psc kscj
denote the marginal probabili-
ties, and is the joint probability.
From Table 2, it can be concluded that the consistence
between the resulting clusters by NMF and those by
k-means depends on the number of clusters (k). This in-
dicates that the clusters by two approaches are different
while having some common grounds. Compared to oth-
ers, the eight clusters seem to have achieved a good per-
formance (except for two clusters, which do not make
much sense). This is supported by the visualization re-
sults in Section 3.
7. Conclusions
Clustering the message data posted on a student discus-
sion forum assists instructors to better understand their
students. In this paper, we have presented an approach to
clustering message data, together with graph visualiza-
tion of the relations among students and their discussion
issues. Experiments have been conducted to demonstrate
the effectiveness of the approaches. The resulting clus-
ters by the approaches are able to disclose the underlying
factors that explain the observed message data for peda-
gogical purposes. Future work includes experiments on
more sets of data.
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