<s>
Vector	B-Algorithm
quantization	I-Algorithm
(	O
VQ	O
)	O
is	O
a	O
classical	O
quantization	B-Algorithm
technique	O
from	O
signal	O
processing	O
that	O
allows	O
the	O
modeling	O
of	O
probability	O
density	O
functions	O
by	O
the	O
distribution	O
of	O
prototype	O
vectors	O
.	O
</s>
<s>
It	O
was	O
originally	O
used	O
for	O
data	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
Each	O
group	O
is	O
represented	O
by	O
its	O
centroid	O
point	O
,	O
as	O
in	O
k-means	B-Algorithm
and	O
some	O
other	O
clustering	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
The	O
density	O
matching	O
property	O
of	O
vector	B-Algorithm
quantization	I-Algorithm
is	O
powerful	O
,	O
especially	O
for	O
identifying	O
the	O
density	O
of	O
large	O
and	O
high-dimensional	O
data	O
.	O
</s>
<s>
This	O
is	O
why	O
VQ	O
is	O
suitable	O
for	O
lossy	B-Algorithm
data	I-Algorithm
compression	I-Algorithm
.	O
</s>
<s>
It	O
can	O
also	O
be	O
used	O
for	O
lossy	B-Algorithm
data	O
correction	O
and	O
density	B-General_Concept
estimation	I-General_Concept
.	O
</s>
<s>
Vector	B-Algorithm
quantization	I-Algorithm
is	O
based	O
on	O
the	O
competitive	B-Algorithm
learning	I-Algorithm
paradigm	O
,	O
so	O
it	O
is	O
closely	O
related	O
to	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
model	O
and	O
to	O
sparse	O
coding	O
models	O
used	O
in	O
deep	B-Algorithm
learning	I-Algorithm
algorithms	O
such	O
as	O
autoencoder	B-Algorithm
.	O
</s>
<s>
The	O
simplest	O
training	O
algorithm	O
for	O
vector	B-Algorithm
quantization	I-Algorithm
is	O
:	O
</s>
<s>
It	O
is	O
desirable	O
to	O
use	O
a	O
cooling	O
schedule	O
to	O
produce	O
convergence	O
:	O
see	O
Simulated	B-Algorithm
annealing	I-Algorithm
.	O
</s>
<s>
Another	O
(	O
simpler	O
)	O
method	O
is	O
LBG	B-Algorithm
which	O
is	O
based	O
on	O
K-Means	B-Algorithm
.	O
</s>
<s>
Vector	B-Algorithm
quantization	I-Algorithm
is	O
used	O
for	O
lossy	B-Algorithm
data	I-Algorithm
compression	I-Algorithm
,	O
lossy	B-Algorithm
data	O
correction	O
,	O
pattern	O
recognition	O
,	O
density	B-General_Concept
estimation	I-General_Concept
and	O
clustering	B-Algorithm
.	O
</s>
<s>
Lossy	B-Algorithm
data	O
correction	O
,	O
or	O
prediction	O
,	O
is	O
used	O
to	O
recover	O
data	O
missing	O
from	O
some	O
dimensions	O
.	O
</s>
<s>
For	O
density	B-General_Concept
estimation	I-General_Concept
,	O
the	O
area/volume	O
that	O
is	O
closer	O
to	O
a	O
particular	O
centroid	O
than	O
to	O
any	O
other	O
is	O
inversely	O
proportional	O
to	O
the	O
density	O
(	O
due	O
to	O
the	O
density	O
matching	O
property	O
of	O
the	O
algorithm	O
)	O
.	O
</s>
<s>
Vector	B-Algorithm
quantization	I-Algorithm
,	O
also	O
called	O
"	O
block	O
quantization	B-Algorithm
"	O
or	O
"	O
pattern	O
matching	O
quantization	B-Algorithm
"	O
is	O
often	O
used	O
in	O
lossy	B-Algorithm
data	I-Algorithm
compression	I-Algorithm
.	O
</s>
<s>
Due	O
to	O
the	O
density	O
matching	O
property	O
of	O
vector	B-Algorithm
quantization	I-Algorithm
,	O
the	O
compressed	B-General_Concept
data	I-General_Concept
has	O
errors	O
that	O
are	O
inversely	O
proportional	O
to	O
density	O
.	O
</s>
<s>
The	O
transformation	O
is	O
usually	O
done	O
by	O
projection	O
or	O
by	O
using	O
a	O
codebook	B-Algorithm
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
a	O
codebook	B-Algorithm
can	O
be	O
also	O
used	O
to	O
entropy	B-Algorithm
code	I-Algorithm
the	O
discrete	O
value	O
in	O
the	O
same	O
step	O
,	O
by	O
generating	O
a	O
prefix	O
coded	O
variable-length	O
encoded	O
value	O
as	O
its	O
output	O
.	O
</s>
<s>
Only	O
the	O
index	O
of	O
the	O
codeword	O
in	O
the	O
codebook	B-Algorithm
is	O
sent	O
instead	O
of	O
the	O
quantized	O
values	O
.	O
</s>
<s>
Twin	O
vector	B-Algorithm
quantization	I-Algorithm
(	O
VQF	B-Algorithm
)	O
is	O
part	O
of	O
the	O
MPEG-4	B-Algorithm
standard	O
dealing	O
with	O
time	O
domain	O
weighted	O
interleaved	O
vector	B-Algorithm
quantization	I-Algorithm
.	O
</s>
<s>
The	O
usage	O
of	O
video	O
codecs	O
based	O
on	O
vector	B-Algorithm
quantization	I-Algorithm
has	O
declined	O
significantly	O
in	O
favor	O
of	O
those	O
based	O
on	O
motion	O
compensated	O
prediction	O
combined	O
with	O
transform	O
coding	O
,	O
e.g.	O
</s>
<s>
those	O
defined	O
in	O
MPEG	O
standards	O
,	O
as	O
the	O
low	O
decoding	O
complexity	O
of	O
vector	B-Algorithm
quantization	I-Algorithm
has	O
become	O
less	O
relevant	O
.	O
</s>
<s>
VQ	O
was	O
also	O
used	O
in	O
the	O
eighties	O
for	O
speech	O
and	O
speaker	B-Application
recognition	I-Application
.	O
</s>
<s>
In	O
pattern	O
recognition	O
applications	O
,	O
one	O
codebook	B-Algorithm
is	O
constructed	O
for	O
each	O
class	O
(	O
each	O
class	O
being	O
a	O
user	O
in	O
biometric	O
applications	O
)	O
using	O
acoustic	O
vectors	O
of	O
this	O
user	O
.	O
</s>
<s>
In	O
the	O
testing	O
phase	O
the	O
quantization	B-Algorithm
distortion	O
of	O
a	O
testing	O
signal	O
is	O
worked	O
out	O
with	O
the	O
whole	O
set	O
of	O
codebooks	B-Algorithm
obtained	O
in	O
the	O
training	O
phase	O
.	O
</s>
<s>
The	O
codebook	B-Algorithm
that	O
provides	O
the	O
smallest	O
vector	B-Algorithm
quantization	I-Algorithm
distortion	O
indicates	O
the	O
identified	O
user	O
.	O
</s>
<s>
The	O
main	O
advantage	O
of	O
VQ	O
in	O
pattern	O
recognition	O
is	O
its	O
low	O
computational	O
burden	O
when	O
compared	O
with	O
other	O
techniques	O
such	O
as	O
dynamic	B-Algorithm
time	I-Algorithm
warping	I-Algorithm
(	O
DTW	O
)	O
and	O
hidden	O
Markov	O
model	O
(	O
HMM	O
)	O
.	O
</s>
<s>
In	O
order	O
to	O
overcome	O
this	O
problem	O
a	O
multi-section	O
codebook	B-Algorithm
approach	O
has	O
been	O
proposed	O
.	O
</s>
<s>
The	O
multi-section	O
approach	O
consists	O
of	O
modelling	O
the	O
signal	O
with	O
several	O
sections	O
(	O
for	O
instance	O
,	O
one	O
codebook	B-Algorithm
for	O
the	O
initial	O
part	O
,	O
another	O
one	O
for	O
the	O
center	O
and	O
a	O
last	O
codebook	B-Algorithm
for	O
the	O
ending	O
part	O
)	O
.	O
</s>
<s>
As	O
VQ	O
is	O
seeking	O
for	O
centroids	O
as	O
density	O
points	O
of	O
nearby	O
lying	O
samples	O
,	O
it	O
can	O
be	O
also	O
directly	O
used	O
as	O
a	O
prototype-based	O
clustering	B-Algorithm
method	O
:	O
each	O
centroid	O
is	O
then	O
associated	O
with	O
one	O
prototype	O
.	O
</s>
<s>
By	O
aiming	O
to	O
minimize	O
the	O
expected	O
squared	O
quantization	B-Algorithm
error	O
and	O
introducing	O
a	O
decreasing	O
learning	O
gain	O
fulfilling	O
the	O
Robbins-Monro	O
conditions	O
,	O
multiple	O
iterations	O
over	O
the	O
whole	O
data	O
set	O
with	O
a	O
concrete	O
but	O
fixed	O
number	O
of	O
prototypes	O
converges	O
to	O
the	O
solution	O
of	O
k-means	B-Algorithm
clustering	I-Algorithm
algorithm	I-Algorithm
in	O
an	O
incremental	O
manner	O
.	O
</s>
<s>
VQ	O
has	O
been	O
used	O
to	O
quantize	O
a	O
feature	O
representation	O
layer	O
in	O
the	O
discriminator	O
of	O
Generative	B-Algorithm
adversarial	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
The	O
feature	O
quantization	B-Algorithm
(	O
FQ	O
)	O
technique	O
performs	O
implicit	O
feature	O
matching	O
.	O
</s>
