<s>
In	O
statistics	O
,	O
a	O
varimax	B-Algorithm
rotation	I-Algorithm
is	O
used	O
to	O
simplify	O
the	O
expression	O
of	O
a	O
particular	O
sub-space	O
in	O
terms	O
of	O
just	O
a	O
few	O
major	O
items	O
each	O
.	O
</s>
<s>
The	O
actual	O
coordinate	O
system	O
is	O
unchanged	O
,	O
it	O
is	O
the	O
orthogonal	B-Application
basis	O
that	O
is	O
being	O
rotated	O
to	O
align	O
with	O
those	O
coordinates	O
.	O
</s>
<s>
The	O
sub-space	O
found	O
with	O
principal	B-Application
component	I-Application
analysis	I-Application
or	O
factor	O
analysis	O
is	O
expressed	O
as	O
a	O
dense	O
basis	O
with	O
many	O
non-zero	O
weights	O
which	O
makes	O
it	O
hard	O
to	O
interpret	O
.	O
</s>
<s>
Varimax	B-Algorithm
is	O
so	O
called	O
because	O
it	O
maximizes	O
the	O
sum	O
of	O
the	O
variances	O
of	O
the	O
squared	O
loadings	O
(	O
squared	O
correlations	O
between	O
variables	O
and	O
factors	O
)	O
.	O
</s>
<s>
Preserving	O
orthogonality	B-Application
requires	O
that	O
it	O
is	O
a	O
rotation	O
that	O
leaves	O
the	O
sub-space	O
invariant	O
.	O
</s>
<s>
If	O
these	O
conditions	O
hold	O
,	O
the	O
factor	O
loading	O
matrix	O
is	O
said	O
to	O
have	O
"	O
simple	O
structure	O
,	O
"	O
and	O
varimax	B-Algorithm
rotation	I-Algorithm
brings	O
the	O
loading	O
matrix	O
closer	O
to	O
such	O
simple	O
structure	O
(	O
as	O
much	O
as	O
the	O
data	O
allow	O
)	O
.	O
</s>
<s>
From	O
the	O
perspective	O
of	O
individuals	O
measured	O
on	O
the	O
variables	O
,	O
varimax	B-Algorithm
seeks	O
a	O
basis	O
that	O
most	O
economically	O
represents	O
each	O
individual	O
—	O
that	O
is	O
,	O
each	O
individual	O
can	O
be	O
well	O
described	O
by	O
a	O
linear	O
combination	O
of	O
only	O
a	O
few	O
basis	O
functions	O
.	O
</s>
<s>
One	O
way	O
of	O
expressing	O
the	O
varimax	B-Algorithm
criterion	O
formally	O
is	O
this	O
:	O
</s>
<s>
it	O
is	O
a	O
popular	O
scheme	O
for	O
orthogonal	B-Application
rotation	O
(	O
where	O
all	O
factors	O
remain	O
uncorrelated	O
with	O
one	O
another	O
)	O
.	O
</s>
<s>
A	O
summary	O
of	O
the	O
use	O
of	O
varimax	B-Algorithm
rotation	I-Algorithm
and	O
of	O
other	O
types	O
of	O
factor	O
rotation	O
is	O
presented	O
in	O
this	O
article	O
on	O
factor	O
analysis	O
.	O
</s>
<s>
In	O
the	O
R	B-Language
programming	I-Language
language	I-Language
the	O
varimax	B-Algorithm
method	O
is	O
implemented	O
in	O
several	O
packages	O
including	O
stats	O
(	O
function	O
varimax( )	O
)	O
,	O
or	O
in	O
contributed	O
packages	O
including	O
GPArotation	O
or	O
psych	O
.	O
</s>
<s>
In	O
SAS	B-Language
varimax	B-Algorithm
rotation	I-Algorithm
is	O
available	O
in	O
PROC	O
FACTOR	O
using	O
ROTATE	O
=	O
VARIMAX	B-Algorithm
.	O
</s>
