Web-based Learning Solutions for Communities of Practice

Mining Unnoticed Knowledge in Collaboration Support Systems
into a larger one, and those that split a larger
cluster into smaller ones. As reported in (Ding &
He, 2002), the MinMax linkage (Ding, He, Zha,
Gu & Simon, 2001) is the best in agglomerative
clustering and the average similarity is the best
method in divisive clustering.
1. In MinMax given n data objects the pairwise
similarity matrix W=(w ij ) (where w ij is the
similarity between i,j) we want to partition
the data into two clusters C 1 ,C 2 using the
min-max principle - minimize similarity
between clusters and maximize similarity
within a cluster. The similarity between C 1
and C 2 is defined as s(C 1 ,C 2 ). Linkage l is
the closeness or similarity measure between
two clusters and helps in getting better results
for clusters. It is defined as follows:
l MinMax (C 1 ,C 2 ) = s(C 1 ,C 2 )/s(C 1 , C 1 )s(C 2 , C 2 )
2. The average similarity is based on the minmax
clustering principle. The purpose here
is to choose the loosest cluster to split, or in
other words the cluster with the smallest average
similarity. The self-similarity of cluster
C is s(C ,C )=s which has to be maximized
k k k kk
during clustering. The average self-similarity
now is computed as skk = skk / nk
2 where
n = |C |. When a cluster has large average
k k
self-similarity then its objects are more
homogeneous.
Directed arrays
If we consider that there is a difference between
the meaning of Xij and Xji, then we understand
that the Euclidean distance between users does
not exist and we have to focus on a directed graph
of users. More precisely, we need a clustering
technique for directed graph in order to optimize
the separation of users into clusters. An array X
may correspond to a community of spaces or to a
space. The commonly used approach is to obtain
the symmetric array X of data and then apply
clustering to X . In our case, we propose the
framework of clustering by weighed cuts directly
in X (Meila & Pentney, 2007). This framework
unifies many different criteria used successfully
on undirected graphs (like the normalization cut
and the averaged cut) and directed graphs. It
formulates clustering as an optimization problem
where the objective is to minimize the weighted
cut in the directed graph which can be equivalent
to the problem of a symmetric matrix.
A different approach, that could probably
lead to better (in a semantic sense) results would
be to use the clustering algorithm presented in
(Chakrabarti, Dom, Gibson, Kumar, Raghavan,
Rajagopalan & Tomkins, 1998); to do that, we
have to consider X as an adjacency matrix of an
underlying graph, with nodes as the users. This
algorithm inspired by the web search algorithm
of (Kleinberg, 1999) can produce clusters, where
in each cluster each user is characterized by two
different scores. The first score (authority score)
depicts the quality of the incoming links a user
has, while the second score (hub score) depicts the
quality of the outgoing links a user has. Hence,
the first score can be used to depict how strong or
weak author is a user and the second score can be
used to depict how good or bad reviewer is this
user. Users that have high authority scores are
expected to have relevant ideas, whereas users
with high hub scores are expected to have worked
in spaces of relevant subject.
Social Network Analysis
The final scope of this analysis involves the mapping
and measuring of the normally unnoticed
relationships between users and, more specifically,
between clusters of users. The presented metrics
are largely regarded as a means of evaluating
properties of particular interest. Even though it
is not the goal of this paper to thoroughly study
the different algorithmic and implementation
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