
148 Knowledge Discovery from Data Streams
m-dimensional space is given by:
vol (c
i
, m) =
π
m
2
r
m
Γ
m
2
+ 1
(9.3)
where Γ is the gamma function:
Γ
m
2
+ 1
=
m
2
!, for even m;
√
π
m!!
2
(m+1)/2
, for odd m.
(9.4)
This criterion may not be applicable to datasets with a large number of
attributes, once as m increases, vol (c
i
, m) tends to zero (Stibor et al.,
2006).
• Sum of squares of distances between examples and centroid
divided by the number of examples. The sum of squares of distances
between examples belonging to c
i
and the centroid µ
i
is given by:
d (x
j
, µ
i
) =
X
x
j
∈c
i
(x
j
− µ
i
)
2
(9.5)
Dividing it by the number of examples that belong to cluster c
i
, we
obtain a comparable ...