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臺大管理論叢
第
27
卷第
2S
期
43
Table 7 shows the user-specified parameters used in the SFC algorithm. We elaborate
these steps in Sections 3.3.1 to 3.3.5.
Table 7 The Parameters Used in the SFC Algorithm
Parameter
Description
Range
w
weight used in distance measure
0≤
w
≤1
ξ
multiplier for determining the number of initial clusters
0≤
ξ
≤1
δ
multiplier for determination to merge clusters or not
δ
≥1
3.3.1 Step 1: Initialize the Representative FU2Ps for the Full Set of FU2Ps
The modified
k
-medoids algorithm requires an initial set of medoids to perform the
clustering process. The number of the initial medoids, denoted as #
Imedoids
, is calculated by
multiplying the number of FU2Ps with
ξ
. The initial medoids are determined by the
Dist
Sum
of
each FU2P. The
Dist
Sum
of a FU2P
i
is the sum of the distances between
i
and the other
FU2Ps, which is defined as follows:
(5)
N
is the number of FU2Ps, and
Dist(i, j)
is the distance between FU2Ps
i
and
j
derived
by using equation (4). The FU2Ps are ordered in ascending order according to their
Dist
Sum
.
The initial set of medoids comprises the first #
Imedoids
ordered FU2Ps.
3.3.2 Step 2: Performing the Modified
k
-medoids Algorithm on the Full Set of FU2Ps
After determining the initial set of medoids, we apply the modified
k
-medoids algorithm
to the full set of FU2Ps. The modified
k
-medoids algorithm is modified from the PAM
algorithm (Han, Kamber, and Pei, 2011). In the PAM algorithm, all pairs of medoids and
non-medoid objects are evaluated to find new medoids at each iteration. However, the time
complexity of the PAM algorithm is too high to cluster a large number of objects. Because
the number of FU2Ps is usually quietly large, we made modifications by only considering
the objects in a cluster to find a new medoid for the cluster. This strategy is similar to the one
used by the
k
-means clustering algorithm. Figure 2 presents the formal algorithm of the
modified
k
-medoids algorithm. At each iteration, the modified
k
-medoid algorithm first tries
to find a new medoid for each cluster. If all medoids remain unchanged, this set of medoids
is returned. If any cluster changes its medoid, the modified
k
-medoid algorithm reassigns
each object to the cluster of this object's nearest medoid.