<s>
Ordination	B-Algorithm
or	O
gradient	B-Algorithm
analysis	I-Algorithm
,	O
in	O
multivariate	O
analysis	O
,	O
is	O
a	O
method	O
complementary	O
to	O
data	B-Algorithm
clustering	I-Algorithm
,	O
and	O
used	O
mainly	O
in	O
exploratory	B-General_Concept
data	I-General_Concept
analysis	I-General_Concept
(	O
rather	O
than	O
in	O
hypothesis	O
testing	O
)	O
.	O
</s>
<s>
In	O
contrast	O
to	O
cluster	B-Algorithm
analysis	I-Algorithm
,	O
ordination	B-Algorithm
orders	O
quantities	O
in	O
a	O
(	O
usually	O
lower-dimensional	O
)	O
latent	O
space	O
.	O
</s>
<s>
In	O
the	O
ordination	B-Algorithm
space	O
,	O
quantities	O
that	O
are	O
near	O
each	O
other	O
share	O
attributes	O
(	O
i.e.	O
,	O
are	O
similar	O
to	O
some	O
degree	O
)	O
,	O
and	O
dissimilar	O
objects	O
are	O
farther	O
from	O
each	O
other	O
.	O
</s>
<s>
Such	O
relationships	O
between	O
the	O
objects	O
,	O
on	O
each	O
of	O
several	O
axes	O
or	O
latent	O
variables	O
,	O
are	O
then	O
characterized	O
numerically	O
and/or	O
graphically	O
in	O
a	O
biplot	B-Application
.	O
</s>
<s>
The	O
first	O
ordination	B-Algorithm
method	O
,	O
principal	B-Application
components	I-Application
analysis	I-Application
,	O
was	O
suggested	O
by	O
Karl	O
Pearson	O
in	O
1901	O
.	O
</s>
<s>
Ordination	B-Algorithm
methods	O
can	O
broadly	O
be	O
categorized	O
in	O
eigenvector-	O
,	O
algorithm-	O
,	O
or	O
model-based	O
methods	O
.	O
</s>
<s>
Many	O
classical	O
ordination	B-Algorithm
techniques	O
,	O
including	O
principal	B-Application
components	I-Application
analysis	I-Application
,	O
correspondence	B-Algorithm
analysis	I-Algorithm
(	O
CA	O
)	O
and	O
its	O
derivatives	O
(	O
detrended	B-Algorithm
correspondence	I-Algorithm
analysis	I-Algorithm
,	O
canonical	O
correspondence	B-Algorithm
analysis	I-Algorithm
,	O
and	O
redundancy	O
analysis	O
,	O
belong	O
to	O
the	O
first	O
group	O
.	O
</s>
<s>
The	O
second	O
group	O
includes	O
some	O
distance-based	O
methods	O
such	O
as	O
non-metric	O
multidimensional	O
scaling	O
,	O
and	O
machine	O
learning	O
methods	O
such	O
as	O
T-distributed	B-Algorithm
stochastic	I-Algorithm
neighbor	I-Algorithm
embedding	I-Algorithm
and	O
nonlinear	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
.	O
</s>
<s>
The	O
third	O
group	O
includes	O
model-based	O
ordination	B-Algorithm
methods	O
,	O
which	O
can	O
be	O
considered	O
as	O
multivariate	O
extensions	O
of	O
Generalized	O
Linear	O
Models	O
.	O
</s>
<s>
Model-based	O
ordination	B-Algorithm
methods	O
are	O
more	O
flexible	O
in	O
their	O
application	O
than	O
classical	O
ordination	B-Algorithm
methods	O
,	O
so	O
that	O
it	O
is	O
for	O
example	O
possible	O
to	O
include	O
random-effects	O
.	O
</s>
<s>
Unlike	O
in	O
the	O
aforementioned	O
two	O
groups	O
,	O
there	O
is	O
no	O
(	O
implicit	O
or	O
explicit	O
)	O
distance	O
measure	O
in	O
the	O
ordination	B-Algorithm
.	O
</s>
<s>
These	O
and	O
other	O
assumptions	O
,	O
such	O
as	O
the	O
assumed	O
mean-variance	O
relationship	O
,	O
can	O
be	O
validated	O
with	O
the	O
use	O
of	O
residual	O
diagnostics	O
,	O
unlike	O
in	O
other	O
ordination	B-Algorithm
methods	O
.	O
</s>
<s>
Ordination	B-Algorithm
can	O
be	O
used	O
on	O
the	O
analysis	O
of	O
any	O
set	O
of	O
multivariate	O
objects	O
.	O
</s>
