<s>
Count	B-Algorithm
sketch	I-Algorithm
is	O
a	O
type	O
of	O
dimensionality	B-Algorithm
reduction	I-Algorithm
that	O
is	O
particularly	O
efficient	O
in	O
statistics	O
,	O
machine	O
learning	O
and	O
algorithms	O
.	O
</s>
<s>
The	O
sketch	O
is	O
nearly	O
identical	O
to	O
the	O
Feature	B-Algorithm
hashing	I-Algorithm
algorithm	O
by	O
John	O
Moody	O
,	O
but	O
differs	O
in	O
its	O
use	O
of	O
hash	O
functions	O
with	O
low	O
dependence	O
,	O
which	O
makes	O
it	O
more	O
practical	O
.	O
</s>
<s>
In	O
order	O
to	O
still	O
have	O
a	O
high	O
probability	O
of	O
success	O
,	O
the	O
median	O
trick	O
is	O
used	O
to	O
aggregate	O
multiple	O
count	B-Algorithm
sketches	I-Algorithm
,	O
rather	O
than	O
the	O
mean	O
.	O
</s>
<s>
These	O
properties	O
allow	O
use	O
for	O
explicit	O
kernel	B-Algorithm
methods	I-Algorithm
,	O
bilinear	O
pooling	B-General_Concept
in	O
neural	B-Architecture
networks	I-Architecture
and	O
is	O
a	O
cornerstone	O
in	O
many	O
numerical	O
linear	O
algebra	O
algorithms	O
.	O
</s>
<s>
The	O
count	B-Algorithm
sketch	I-Algorithm
projection	O
of	O
the	O
outer	O
product	O
of	O
two	O
vectors	O
is	O
equivalent	O
to	O
the	O
convolution	B-Language
of	O
two	O
component	O
count	B-Algorithm
sketches	I-Algorithm
.	O
</s>
<s>
,	O
where	O
and	O
are	O
independent	O
count	B-Algorithm
sketch	I-Algorithm
matrices	O
.	O
</s>
<s>
Pham	O
and	O
Pagh	O
show	O
that	O
this	O
equals	O
–	O
a	O
count	B-Algorithm
sketch	I-Algorithm
of	O
the	O
outer	O
product	O
of	O
vectors	O
,	O
where	O
denotes	O
Kronecker	O
product	O
.	O
</s>
<s>
The	O
fast	O
Fourier	O
transform	O
can	O
be	O
used	O
to	O
do	O
fast	O
convolution	B-Language
of	O
count	B-Algorithm
sketches	I-Algorithm
.	O
</s>
