<s>
CURE	O
(	O
Clustering	O
Using	O
REpresentatives	O
)	O
is	O
an	O
efficient	O
data	B-Algorithm
clustering	I-Algorithm
algorithm	O
for	O
large	O
databases	O
.	O
</s>
<s>
Compared	O
with	O
K-means	B-Algorithm
clustering	I-Algorithm
it	O
is	O
more	O
robust	O
to	O
outliers	O
and	O
able	O
to	O
identify	O
clusters	O
having	O
non-spherical	O
shapes	O
and	O
size	O
variances	O
.	O
</s>
<s>
The	O
popular	O
K-means	B-Algorithm
clustering	I-Algorithm
algorithm	I-Algorithm
minimizes	O
the	O
sum	O
of	O
squared	O
errors	O
criterion	O
:	O
</s>
<s>
Also	O
,	O
with	O
hierarchic	O
clustering	B-Algorithm
algorithms	I-Algorithm
these	O
problems	O
exist	O
as	O
none	O
of	O
the	O
distance	O
measures	O
between	O
clusters	O
(	O
)	O
tend	O
to	O
work	O
with	O
different	O
cluster	O
shapes	O
.	O
</s>
<s>
Also	O
the	O
running	B-General_Concept
time	I-General_Concept
is	O
high	O
when	O
n	O
is	O
large	O
.	O
</s>
<s>
The	O
problem	O
with	O
the	O
BIRCH	B-Algorithm
algorithm	I-Algorithm
is	O
that	O
once	O
the	O
clusters	O
are	O
generated	O
after	O
step	O
3	O
,	O
it	O
uses	O
centroids	O
of	O
the	O
clusters	O
and	O
assigns	O
each	O
data	B-Application
point	I-Application
to	O
the	O
cluster	O
with	O
the	O
closest	O
centroid	O
.	O
</s>
<s>
To	O
avoid	O
the	O
problems	O
with	O
non-uniform	O
sized	O
or	O
shaped	O
clusters	O
,	O
CURE	O
employs	O
a	O
hierarchical	B-Algorithm
clustering	I-Algorithm
algorithm	O
that	O
adopts	O
a	O
middle	O
ground	O
between	O
the	O
centroid	O
based	O
and	O
all	O
point	O
extremes	O
.	O
</s>
<s>
The	O
clusters	O
with	O
the	O
closest	O
pair	O
of	O
representatives	O
are	O
the	O
clusters	O
that	O
are	O
merged	O
at	O
each	O
step	O
of	O
CURE	O
's	O
hierarchical	B-Algorithm
clustering	I-Algorithm
algorithm	O
.	O
</s>
<s>
Running	B-General_Concept
time	I-General_Concept
is	O
O(n2 log n )	O
,	O
making	O
it	O
rather	O
expensive	O
,	O
and	O
space	O
complexity	O
is	O
O(n )	O
.	O
</s>
<s>
Labeling	O
data	O
on	O
disk	O
:	O
Given	O
only	O
representative	O
points	O
for	O
k	O
clusters	O
,	O
the	O
remaining	O
data	B-Application
points	I-Application
are	O
also	O
assigned	O
to	O
the	O
clusters	O
.	O
</s>
<s>
For	O
this	O
a	O
fraction	O
of	O
randomly	O
selected	O
representative	O
points	O
for	O
each	O
of	O
the	O
k	O
clusters	O
is	O
chosen	O
and	O
data	B-Application
point	I-Application
is	O
assigned	O
to	O
the	O
cluster	O
containing	O
the	O
representative	O
point	O
closest	O
to	O
it	O
.	O
</s>
<s>
For	O
every	O
cluster	O
u	O
(	O
each	O
input	O
point	O
)	O
,	O
in	O
u.mean	O
and	O
u.rep	O
store	O
the	O
mean	O
of	O
the	O
points	O
in	O
the	O
cluster	O
and	O
a	O
set	O
of	O
c	O
representative	O
points	O
of	O
the	O
cluster	O
(	O
initially	O
c	O
=	O
1	O
since	O
each	O
cluster	O
has	O
one	O
data	B-Application
point	I-Application
)	O
.	O
</s>
<s>
open	O
source	O
library	O
includes	O
a	O
Python	O
and	O
C++	O
implementation	O
of	O
CURE	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
