<s>
In	O
theoretical	O
computer	O
science	O
and	O
the	O
study	O
of	O
machine	O
learning	O
,	O
the	O
manifold	B-General_Concept
hypothesis	I-General_Concept
is	O
the	O
hypothesis	O
that	O
many	O
high-dimensional	O
data	O
sets	O
that	O
occur	O
in	O
the	O
real	O
world	O
actually	O
lie	O
along	O
low-dimensional	O
latent	B-Algorithm
manifolds	I-Algorithm
inside	O
that	O
high-dimensional	O
space	O
.	O
</s>
<s>
As	O
a	O
consequence	O
of	O
the	O
manifold	B-General_Concept
hypothesis	I-General_Concept
,	O
many	O
data	O
sets	O
that	O
appear	O
to	O
initially	O
require	O
many	O
variables	O
to	O
describe	O
,	O
can	O
actually	O
be	O
described	O
by	O
a	O
comparatively	O
small	O
number	O
of	O
variables	O
,	O
likened	O
to	O
the	O
local	O
coordinate	O
system	O
of	O
the	O
underlying	O
manifold	O
.	O
</s>
<s>
The	O
manifold	B-General_Concept
hypothesis	I-General_Concept
is	O
related	O
to	O
the	O
effectiveness	O
of	O
nonlinear	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
techniques	O
in	O
machine	O
learning	O
.	O
</s>
<s>
Many	O
techniques	O
of	O
dimensional	O
reduction	O
make	O
the	O
assumption	O
that	O
data	O
lies	O
along	O
a	O
low-dimensional	O
submanifold	O
,	O
such	O
as	O
manifold	O
sculpting	O
,	O
manifold	B-Algorithm
alignment	I-Algorithm
,	O
and	O
manifold	B-General_Concept
regularization	I-General_Concept
.	O
</s>
