<s>
In	O
statistics	O
,	O
Ward	B-Algorithm
's	I-Algorithm
method	I-Algorithm
is	O
a	O
criterion	O
applied	O
in	O
hierarchical	B-Algorithm
cluster	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Ward	O
's	O
minimum	O
variance	O
method	O
is	O
a	O
special	O
case	O
of	O
the	O
objective	O
function	O
approach	O
originally	O
presented	O
by	O
Joe	O
H	O
.	O
Ward	O
,	O
Jr.	O
Ward	O
suggested	O
a	O
general	O
agglomerative	B-Algorithm
hierarchical	I-Algorithm
clustering	I-Algorithm
procedure	O
,	O
where	O
the	O
criterion	O
for	O
choosing	O
the	O
pair	O
of	O
clusters	O
to	O
merge	O
at	O
each	O
step	O
is	O
based	O
on	O
the	O
optimal	O
value	O
of	O
an	O
objective	O
function	O
.	O
</s>
<s>
To	O
illustrate	O
the	O
procedure	O
,	O
Ward	O
used	O
the	O
example	O
where	O
the	O
objective	O
function	O
is	O
the	O
error	B-General_Concept
sum	I-General_Concept
of	I-General_Concept
squares	I-General_Concept
,	O
and	O
this	O
example	O
is	O
known	O
as	O
Ward	B-Algorithm
's	I-Algorithm
method	I-Algorithm
or	O
more	O
precisely	O
Ward	O
's	O
minimum	O
variance	O
method	O
.	O
</s>
<s>
The	O
nearest-neighbor	B-Algorithm
chain	I-Algorithm
algorithm	I-Algorithm
can	O
be	O
used	O
to	O
find	O
the	O
same	O
clustering	O
defined	O
by	O
Ward	B-Algorithm
's	I-Algorithm
method	I-Algorithm
,	O
in	O
time	O
proportional	O
to	O
the	O
size	O
of	O
the	O
input	O
distance	O
matrix	O
and	O
space	O
linear	O
in	O
the	O
number	O
of	O
points	O
being	O
clustered	O
.	O
</s>
<s>
Note	O
:	O
In	O
software	O
that	O
implements	O
Ward	B-Algorithm
's	I-Algorithm
method	I-Algorithm
,	O
it	O
is	O
important	O
to	O
check	O
whether	O
the	O
function	O
arguments	O
should	O
specify	O
Euclidean	O
distances	O
or	O
squared	O
Euclidean	O
distances	O
.	O
</s>
<s>
The	O
Lance	O
–	O
Williams	O
algorithms	O
are	O
an	O
infinite	O
family	O
of	O
agglomerative	B-Algorithm
hierarchical	I-Algorithm
clustering	I-Algorithm
algorithms	O
which	O
are	O
represented	O
by	O
a	O
recursive	O
formula	O
for	O
updating	O
cluster	O
distances	O
at	O
each	O
step	O
(	O
each	O
time	O
a	O
pair	O
of	O
clusters	O
is	O
merged	O
)	O
.	O
</s>
<s>
Several	O
standard	O
clustering	O
algorithms	O
such	O
as	O
single	B-Algorithm
linkage	I-Algorithm
,	O
complete	B-Algorithm
linkage	I-Algorithm
,	O
and	O
group	O
average	O
method	O
have	O
a	O
recursive	O
formula	O
of	O
the	O
above	O
type	O
.	O
</s>
<s>
A	O
table	O
of	O
parameters	O
for	O
standard	O
methods	O
is	O
given	O
by	O
several	O
authors.	O
<	O
ref>Cormack	O
,	O
R	O
.	O
M	O
.	O
(	O
1971	O
)	O
,	O
"	O
A	O
Review	O
of	O
Classification	O
"	O
,	O
Journal	O
of	O
the	O
Royal	O
Statistical	O
Society	O
,	O
Series	O
A	O
,	O
134(3 )	O
,	O
321-367.	O
<	O
/ref	O
>Gordon	O
,	O
A	O
.	O
D	O
.	O
(	O
1999	O
)	O
,	O
Classification	O
,	O
2nd	O
Edition	O
,	O
Chapman	O
and	O
Hall	O
,	O
Boca	O
Raton.Milligan	O
,	O
G	O
.	O
W	O
.	O
(	O
1979	O
)	O
,	O
"	O
Ultrametric	O
Hierarchical	B-Algorithm
Clustering	I-Algorithm
Algorithms	O
"	O
,	O
Psychometrika	O
,	O
44(3 )	O
,	O
343	O
–	O
346	O
.	O
</s>
<s>
The	O
popularity	O
of	O
the	O
Ward	B-Algorithm
's	I-Algorithm
method	I-Algorithm
has	O
led	O
to	O
variations	O
of	O
it	O
.	O
</s>
