Biology Reference
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Then the quality of a set of medoids is evaluated by the average modified Man-
hattan segmental distance from the points to the centroids of the clusters to which
they belong.
9.3.3.1.
Simplified Replacing Logic
We propose a simplified replacing logic compared to PROCLUS to decide whether
it's good to replace the bad medoids in the current best medoids set with new
medoids. When replacing the bad medoids, we first calculate
δ
i
for each medoid
m
i
. We only recalculate the
X
i,j
values for those medoids whose
δ
i
values
changed (store the
X
i,j
value for current best objective case so that for those
medoids whose
δ
i
values don't change, their
X
i,j
values can be recovered from
the stored values). Then we calculate
Y
i
,
σ
i
and
Z
i,j
. We decide dimensions for all
clusters by the
Z
i,j
values. When we assign points to clusters, there are two cases.
For the points previously in the clusters whose
δ
values don't change, we only
compare their modified Manhattan segmental distance from the current medoids
with their modified Manhattan segmental distance from the medoids whose
δ
val-
ues changed. For the points previously in the clusters whose
δ
values changed or
in the bad medoid's cluster, we compare its distance to all the current medoids to
decide which cluster it belongs to. Then the new clusters are evaluated to decide
whether the objective value is better. The simplified logic for assigning points in
the iterative phase is given in Algorithm 9.3.
Algorithm
9.3.
IterativeAssignPoints(
C
1
,
...,
C
k
,
D
1
,
D
2
,
...,
D
k
,
B
)
{
B
is the set of medoids whose
d
i
values changed and newly added medoids
}
begin
for
all the points
i
do
assume point
i
∈
C
j
B
then
compare point
i
's modified Manhattan segmental distance with all the
medoids to decide which cluster it belongs to
else
compare point
i
's modified Manhattan segmental distance with all the
medoids
in B
to decide which cluster it belongs to
end if
end for
end
if
C
j
∈
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