<s>
Random	B-Algorithm
indexing	I-Algorithm
is	O
a	O
dimensionality	B-Algorithm
reduction	I-Algorithm
method	O
and	O
computational	O
framework	O
for	O
distributional	O
semantics	O
,	O
based	O
on	O
the	O
insight	O
that	O
very-high-dimensional	O
vector	O
space	O
model	O
implementations	O
are	O
impractical	O
,	O
that	O
models	O
need	O
not	O
grow	O
in	O
dimensionality	O
when	O
new	O
items	O
(	O
e.g.	O
</s>
<s>
This	O
is	O
the	O
original	O
point	O
of	O
the	O
random	B-Architecture
projection	I-Architecture
approach	O
to	O
dimension	B-Algorithm
reduction	I-Algorithm
first	O
formulated	O
as	O
the	O
Johnson	O
–	O
Lindenstrauss	O
lemma	O
,	O
and	O
locality-sensitive	B-Algorithm
hashing	I-Algorithm
has	O
some	O
of	O
the	O
same	O
starting	O
points	O
.	O
</s>
<s>
Random	B-Algorithm
indexing	I-Algorithm
,	O
as	O
used	O
in	O
representation	O
of	O
language	O
,	O
originates	O
from	O
the	O
work	O
of	O
Pentti	O
Kanerva	O
on	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
,	O
and	O
can	O
be	O
described	O
as	O
an	O
incremental	O
formulation	O
of	O
a	O
random	B-Architecture
projection	I-Architecture
.	O
</s>
<s>
It	O
can	O
be	O
also	O
verified	O
that	O
random	B-Algorithm
indexing	I-Algorithm
is	O
a	O
random	B-Architecture
projection	I-Architecture
technique	O
for	O
the	O
construction	O
of	O
Euclidean	O
spaces	O
—	O
i.e.	O
</s>
<s>
In	O
Euclidean	O
spaces	O
,	O
random	B-Architecture
projections	I-Architecture
are	O
elucidated	O
using	O
the	O
Johnson	O
–	O
Lindenstrauss	O
lemma	O
.	O
</s>
<s>
The	O
TopSig	O
technique	O
extends	O
the	O
random	B-Algorithm
indexing	I-Algorithm
model	O
to	O
produce	O
bit	B-Data_Structure
vectors	I-Data_Structure
for	O
comparison	O
with	O
the	O
Hamming	O
distance	O
similarity	O
function	O
.	O
</s>
<s>
It	O
is	O
used	O
for	O
improving	O
the	O
performance	O
of	O
information	B-Library
retrieval	I-Library
and	O
document	O
clustering	O
.	O
</s>
<s>
Many	O
random	B-Algorithm
indexing	I-Algorithm
methods	O
primarily	O
generate	O
similarity	O
from	O
co-occurrence	O
of	O
items	O
in	O
a	O
corpus	O
.	O
</s>
<s>
Reflexive	O
Random	B-Algorithm
Indexing	I-Algorithm
(	O
RRI	O
)	O
generates	O
similarity	O
from	O
co-occurrence	O
and	O
from	O
shared	O
occurrence	O
with	O
other	O
items	O
.	O
</s>
