<s>
Complete-linkage	B-Algorithm
clustering	I-Algorithm
is	O
one	O
of	O
several	O
methods	O
of	O
agglomerative	B-Algorithm
hierarchical	I-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
The	O
result	O
of	O
the	O
clustering	O
can	O
be	O
visualized	O
as	O
a	O
dendrogram	B-Application
,	O
which	O
shows	O
the	O
sequence	O
of	O
cluster	O
fusion	O
and	O
the	O
distance	O
at	O
which	O
each	O
fusion	O
took	O
place	O
.	O
</s>
<s>
The	O
definition	O
of	O
'	O
shortest	O
distance	O
 '	O
is	O
what	O
differentiates	O
between	O
the	O
different	O
agglomerative	B-Algorithm
clustering	I-Algorithm
methods	O
.	O
</s>
<s>
In	O
complete-linkage	B-Algorithm
clustering	I-Algorithm
,	O
the	O
link	O
between	O
two	O
clusters	O
contains	O
all	O
element	O
pairs	O
,	O
and	O
the	O
distance	O
between	O
clusters	O
equals	O
the	O
distance	O
between	O
those	O
two	O
elements	O
(	O
one	O
in	O
each	O
cluster	O
)	O
that	O
are	O
farthest	O
away	O
from	O
each	O
other	O
.	O
</s>
<s>
The	O
following	O
algorithm	O
is	O
an	O
agglomerative	B-Algorithm
scheme	O
that	O
erases	O
rows	O
and	O
columns	O
in	O
a	O
proximity	O
matrix	O
as	O
old	O
clusters	O
are	O
merged	O
into	O
new	O
ones	O
.	O
</s>
<s>
The	O
complete	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
algorithm	O
consists	O
of	O
the	O
following	O
steps	O
:	O
</s>
<s>
In	O
May	O
1976	O
,	O
D	O
.	O
Defays	O
proposed	O
an	O
optimally	O
efficient	O
algorithm	O
of	O
only	O
complexity	O
known	O
as	O
CLINK	O
(	O
published	O
1977	O
)	O
inspired	O
by	O
the	O
similar	O
algorithm	O
SLINK	B-Algorithm
for	O
single-linkage	B-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
This	O
corresponds	O
to	O
the	O
expectation	O
of	O
the	O
ultrametricity	B-Algorithm
hypothesis	O
.	O
</s>
<s>
Because	O
of	O
the	O
ultrametricity	B-Algorithm
constraint	O
,	O
the	O
branches	O
joining	O
or	O
to	O
,	O
and	O
to	O
,	O
are	O
equal	O
and	O
have	O
the	O
following	O
total	O
length	O
:	O
</s>
<s>
The	O
dendrogram	B-Application
is	O
now	O
complete	O
.	O
</s>
<s>
It	O
is	O
ultrametric	B-Algorithm
because	O
all	O
tips	O
(	O
to	O
)	O
are	O
equidistant	O
from	O
:	O
</s>
<s>
The	O
dendrogram	B-Application
is	O
therefore	O
rooted	O
by	O
,	O
its	O
deepest	O
node	O
.	O
</s>
<s>
Alternative	O
linkage	O
schemes	O
include	O
single	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
and	O
average	B-Algorithm
linkage	I-Algorithm
clustering	O
-	O
implementing	O
a	O
different	O
linkage	O
in	O
the	O
naive	O
algorithm	O
is	O
simply	O
a	O
matter	O
of	O
using	O
a	O
different	O
formula	O
to	O
calculate	O
inter-cluster	O
distances	O
in	O
the	O
initial	O
computation	O
of	O
the	O
proximity	O
matrix	O
and	O
in	O
step	O
4	O
of	O
the	O
above	O
algorithm	O
.	O
</s>
<s>
Complete	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
avoids	O
a	O
drawback	O
of	O
the	O
alternative	O
single	B-Algorithm
linkage	I-Algorithm
method	O
-	O
the	O
so-called	O
chaining	O
phenomenon	O
,	O
where	O
clusters	O
formed	O
via	O
single	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
may	O
be	O
forced	O
together	O
due	O
to	O
single	O
elements	O
being	O
close	O
to	O
each	O
other	O
,	O
even	O
though	O
many	O
of	O
the	O
elements	O
in	O
each	O
cluster	O
may	O
be	O
very	O
distant	O
to	O
each	O
other	O
.	O
</s>
<s>
+	O
Comparison	O
of	O
dendrograms	B-Application
obtained	O
under	O
different	O
clustering	O
methods	O
from	O
the	O
same	O
distance	O
matrix	O
.	O
</s>
<s>
Single-linkage	B-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
Complete-linkage	B-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
Average	B-Algorithm
linkage	I-Algorithm
clustering	O
:	O
WPGMA	B-Algorithm
.	O
</s>
<s>
Average	B-Algorithm
linkage	I-Algorithm
clustering	O
:	O
UPGMA	B-Algorithm
.	O
</s>
