Image Processing Reference
In-Depth Information
3. Calculate the threshold value T
m
for the feature f
m
, which maximizes class sep-
arability along that feature.
4. Based on the threshold T
m
, discretize the corresponding feature f
m
of the data
element x
j
as follows
=
1,
if Discretized(f
)≥T
mj
m
f
mj
0,
Otherwise
5. Repeat steps 2 to 4 for all the features and generate the set of discretized objects
X ={x
1
,, x
j
,, x
n
}.
6. Calculate total number of similar discretized objects N(x
i
) and mean of similar
objects v(x
i
) of x
i
as
n
n
1
N(x
i
)
N(x
i
) =
δ
j
and
v(x
i
) =
δ
j
×x
j
j
=1
j
=1
δ
j
=
1
if x
j
= x
i
where
0
Otherwise
7. Sort n objects according to their values of N(x
i
) such that N(x
) > N(x
) >
1
2
> N(x
n
).
8. If x
i
= x
j
, then N(x
i
) = N(x
j
) and v(x
j
) should not be considered as a centroid
(mean), resulting in a reduced set of objects to be considered for initial centroids.
9. Let there be n objects in the reduced set having N(x
i
) values such that N(x
1
) >
N(x
2
) >> N(x
´n
). A heuristic threshold function can be defined as follows
(Banerjee, Mitra, and Pal, 1998):
where R =
´n
R
ǫ
;
1
N(x
i
)−N(x
i+1
)
Tr =
i
=1
where ǫ is a constant (= 0.5, say), so that all the means v(x
i
) of the objects in
reduced set having N(x
i
) value higher than it are regarded as the candidates for
initial centroids (means).
The value of Tr is high if most of the N(x
i
)'s are large and close to each other. The above
condition occurs when a small number of large clusters are present. On the other hand, if
the N(x
i
)'s have wide variation among them, then the number of clusters with smaller size
increases. Accordingly, Tr attains a lower value automatically. Note that the main motive
of introducing this threshold function lies in reducing the number of centroids. Actually,
it attempts to eliminate noisy centroids (data representatives having lower values of N(x
i
))
from the whole data set. The whole approach is, therefore, data dependent.
2.6
Experimental Results and Discussion
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