Databases Reference
In-Depth Information
n
X
For each cluster,
C
j
, 0
<
w
ij
<
n
. This requirement ensures that for every cluster,
i
D1
there is at least one object for which the membership value is nonzero.
Example11.4
Fuzzy clusters
. Suppose the
AllElectronics
online store has six reviews. The keywords
contained in these reviews are listed in Table 11.2.
We can group the reviews into two fuzzy clusters,
C
1
and
C
2
.
C
1
is for “digital camera”
and “lens,” and
C
2
is for “computer.” The partition matrix is
2
4
3
5
1
0
1
0
1
0
M
D
.
2
3
1
3
0
1
0
1
Here, we use the keywords “digital camera” and “lens” as the features of cluster
C
1
, and
“computer” as the feature of cluster
C
2
. For review,
R
i
, and cluster,
C
j
.
1
i
6, 1
j
2
/
,
w
ij
is defined as
j
R
i
\
C
j
j
j
R
i
\.
j
R
i
\
C
j
j
j
R
i
\f
digital camera
,
lens
,
computer
gj
w
ij
D
C
1
[
C
2
/j
D
.
In this fuzzy clustering, review
R
4
belongs to clusters
C
1
and
C
2
with membership
degrees
2
3
1
and
3
, respectively.
“How can we evaluate how well a fuzzy clustering describes a data set?”
Consider a set
of objects,
o
1
,
:::
,
o
n
, and a fuzzy clusteringCof
k
clusters,
C
1
,
:::
,
C
k
. Let
M
D [
w
ij
]
.
1
,
C
k
,
respectively. Here, a center can be defined either as the mean or the medoid, or in other
ways specific to the application.
As discussed in Chapter 10, the distance or similarity between an object and the cen-
ter of the cluster to which the object is assigned can be used to measure how well the
Table11.2
Set of Reviews and the Keywords Used
i
n
, 1
j
k
/
be the partition matrix. Let
c
1
,
:::
,
c
k
be the
centers
of clusters
C
1
,
:::
ReviewID Keywords
R
1
digital camera, lens
R
2
digital camera
R
3
lens
R
4
digital camera, lens, computer
R
5
computer, CPU
R
6
computer, computer game
