<s>
In	O
computer	B-Application
vision	I-Application
,	O
the	O
bag-of-words	B-General_Concept
model	I-General_Concept
(	O
BoW	O
model	O
)	O
sometimes	O
called	O
bag-of-visual-words	O
model	O
can	O
be	O
applied	O
to	O
image	O
classification	O
or	O
retrieval	B-Application
,	O
by	O
treating	O
image	B-Algorithm
features	I-Algorithm
as	O
words	O
.	O
</s>
<s>
In	O
document	B-Algorithm
classification	I-Algorithm
,	O
a	O
bag	B-General_Concept
of	I-General_Concept
words	I-General_Concept
is	O
a	O
sparse	B-Algorithm
vector	I-Algorithm
of	O
occurrence	O
counts	O
of	O
words	O
;	O
that	O
is	O
,	O
a	O
sparse	O
histogram	B-Algorithm
over	O
the	O
vocabulary	O
.	O
</s>
<s>
In	O
computer	B-Application
vision	I-Application
,	O
a	O
bag	B-General_Concept
of	I-General_Concept
visual	I-General_Concept
words	I-General_Concept
is	O
a	O
vector	O
of	O
occurrence	O
counts	O
of	O
a	O
vocabulary	O
of	O
local	O
image	B-Algorithm
features	I-Algorithm
.	O
</s>
<s>
A	O
definition	O
of	O
the	O
BoW	O
model	O
can	O
be	O
the	O
"	O
histogram	B-Algorithm
representation	O
based	O
on	O
independent	O
features	O
"	O
.	O
</s>
<s>
Content	O
based	O
image	O
indexing	O
and	O
retrieval	B-Application
(	O
CBIR	O
)	O
appears	O
to	O
be	O
the	O
early	O
adopter	O
of	O
this	O
image	O
representation	O
technique	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
famous	O
descriptors	O
is	O
Scale-invariant	B-Algorithm
feature	I-Algorithm
transform	I-Algorithm
(	O
SIFT	B-Algorithm
)	O
.	O
</s>
<s>
SIFT	B-Algorithm
converts	O
each	O
patch	O
to	O
128-dimensional	O
vector	O
.	O
</s>
<s>
After	O
this	O
step	O
,	O
each	O
image	O
is	O
a	O
collection	O
of	O
vectors	O
of	O
the	O
same	O
dimension	O
(	O
128	O
for	O
SIFT	B-Algorithm
)	O
,	O
where	O
the	O
order	O
of	O
different	O
vectors	O
is	O
of	O
no	O
importance	O
.	O
</s>
<s>
One	O
simple	O
method	O
is	O
performing	O
k-means	B-Algorithm
clustering	I-Algorithm
over	O
all	O
the	O
vectors	O
.	O
</s>
<s>
Thus	O
,	O
each	O
patch	O
in	O
an	O
image	O
is	O
mapped	O
to	O
a	O
certain	O
codeword	O
through	O
the	O
clustering	O
process	O
and	O
the	O
image	O
can	O
be	O
represented	O
by	O
the	O
histogram	B-Algorithm
of	O
the	O
codewords	O
.	O
</s>
<s>
Computer	B-Application
vision	I-Application
researchers	O
have	O
developed	O
several	O
learning	O
methods	O
to	O
leverage	O
the	O
BoW	O
model	O
for	O
image	O
related	O
tasks	O
,	O
such	O
as	O
object	B-General_Concept
categorization	I-General_Concept
.	O
</s>
<s>
For	O
multiple	O
label	O
categorization	O
problem	O
,	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
can	O
be	O
used	O
as	O
an	O
evaluation	O
metric	O
.	O
</s>
<s>
:	O
each	O
patch	O
is	O
a	O
V-dimensional	O
vector	O
that	O
has	O
a	O
single	O
component	O
equal	O
to	O
one	O
and	O
all	O
other	O
components	O
equal	O
to	O
zero	O
(	O
For	O
k-means	B-Algorithm
clustering	I-Algorithm
setting	O
,	O
the	O
single	O
component	O
equal	O
one	O
indicates	O
the	O
cluster	O
that	O
belongs	O
to	O
)	O
.	O
</s>
<s>
Since	O
the	O
BoW	O
model	O
is	O
an	O
analogy	O
to	O
the	O
BoW	O
model	O
in	O
NLP	O
,	O
generative	O
models	O
developed	O
in	O
text	O
domains	O
can	O
also	O
be	O
adapted	O
in	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
Simple	O
Naïve	B-General_Concept
Bayes	I-General_Concept
model	O
and	O
hierarchical	O
Bayesian	O
models	O
are	O
discussed	O
.	O
</s>
<s>
The	O
simplest	O
one	O
is	O
Naïve	B-General_Concept
Bayes	I-General_Concept
classifier	I-General_Concept
.	O
</s>
<s>
Using	O
the	O
language	O
of	O
graphical	B-Algorithm
models	I-Algorithm
,	O
the	O
Naïve	B-General_Concept
Bayes	I-General_Concept
classifier	I-General_Concept
is	O
described	O
by	O
the	O
equation	O
below	O
.	O
</s>
<s>
Since	O
the	O
Naïve	B-General_Concept
Bayes	I-General_Concept
classifier	I-General_Concept
is	O
simple	O
yet	O
effective	O
,	O
it	O
is	O
usually	O
used	O
as	O
a	O
baseline	O
method	O
for	O
comparison	O
.	O
</s>
<s>
The	O
basic	O
assumption	O
of	O
Naïve	B-General_Concept
Bayes	I-General_Concept
model	O
does	O
not	O
hold	O
sometimes	O
.	O
</s>
<s>
Probabilistic	B-General_Concept
latent	I-General_Concept
semantic	I-General_Concept
analysis	I-General_Concept
(	O
pLSA	B-General_Concept
)	O
and	O
latent	O
Dirichlet	O
allocation	O
(	O
LDA	O
)	O
are	O
two	O
popular	O
topic	O
models	O
from	O
text	O
domains	O
to	O
tackle	O
the	O
similar	O
multiple	O
"	O
theme	O
"	O
problem	O
.	O
</s>
<s>
Since	O
images	O
are	O
represented	O
based	O
on	O
the	O
BoW	O
model	O
,	O
any	O
discriminative	O
model	O
suitable	O
for	O
text	O
document	B-Algorithm
categorization	I-Algorithm
can	O
be	O
tried	O
,	O
such	O
as	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
(	O
SVM	B-Algorithm
)	O
and	O
AdaBoost	B-Algorithm
.	O
</s>
<s>
Kernel	O
trick	O
is	O
also	O
applicable	O
when	O
kernel	O
based	O
classifier	O
is	O
used	O
,	O
such	O
as	O
SVM	B-Algorithm
.	O
</s>
<s>
Pyramid	O
match	O
kernel	O
is	O
a	O
fast	O
algorithm	O
(	O
linear	O
complexity	O
instead	O
of	O
classic	O
one	O
in	O
quadratic	O
complexity	O
)	O
kernel	O
function	O
(	O
satisfying	O
Mercer	O
's	O
condition	O
)	O
which	O
maps	O
the	O
BoW	O
features	O
,	O
or	O
set	O
of	O
features	O
in	O
high	O
dimension	O
,	O
to	O
multi-dimensional	O
multi-resolution	O
histograms	B-Algorithm
.	O
</s>
<s>
An	O
advantage	O
of	O
these	O
multi-resolution	O
histograms	B-Algorithm
is	O
their	O
ability	O
to	O
capture	O
co-occurring	O
features	O
.	O
</s>
<s>
The	O
pyramid	O
match	O
kernel	O
builds	O
multi-resolution	O
histograms	B-Algorithm
by	O
binning	O
data	O
points	O
into	O
discrete	O
regions	O
of	O
increasing	O
size	O
.	O
</s>
<s>
Instead	O
,	O
it	O
intersects	O
the	O
histograms	B-Algorithm
to	O
approximate	O
the	O
optimal	O
match	O
.	O
</s>
<s>
For	O
feature	O
level	O
improvements	O
,	O
correlogram	B-Application
features	O
can	O
capture	O
spatial	O
co-occurrences	O
of	O
features	O
.	O
</s>
<s>
The	O
hierarchical	O
shape	O
and	O
appearance	O
model	O
for	O
human	O
action	O
introduces	O
a	O
new	O
part	O
layer	O
(	O
Constellation	B-General_Concept
model	I-General_Concept
)	O
between	O
the	O
mixture	O
proportion	O
and	O
the	O
BoW	O
features	O
,	O
which	O
captures	O
the	O
spatial	O
relationships	O
among	O
parts	O
in	O
the	O
layer	O
.	O
</s>
<s>
For	O
discriminative	O
models	O
,	O
spatial	O
pyramid	O
match	O
performs	O
pyramid	O
matching	O
by	O
partitioning	O
the	O
image	O
into	O
increasingly	O
fine	O
sub-regions	O
and	O
compute	O
histograms	B-Algorithm
of	O
local	O
features	O
inside	O
each	O
sub-region	O
.	O
</s>
<s>
SIFT	B-Algorithm
)	O
by	O
their	O
spatial	O
coordinates	O
normalised	O
by	O
the	O
image	O
width	O
and	O
height	O
have	O
proved	O
to	O
be	O
a	O
robust	O
and	O
simple	O
Spatial	O
Coordinate	O
Coding	O
approach	O
which	O
introduces	O
spatial	O
information	O
to	O
the	O
BoW	O
model	O
.	O
</s>
<s>
Moreover	O
,	O
a	O
recent	O
detailed	O
comparison	O
of	O
coding	O
and	O
pooling	O
methods	O
for	O
BoW	O
has	O
showed	O
that	O
second	O
order	O
statistics	O
combined	O
with	O
Sparse	O
Coding	O
and	O
an	O
appropriate	O
pooling	O
such	O
as	O
Power	O
Normalisation	O
can	O
further	O
outperform	O
Fisher	O
Vectors	O
and	O
even	O
approach	O
results	O
of	O
simple	O
models	O
of	O
Convolutional	B-Architecture
Neural	I-Architecture
Network	I-Architecture
on	O
some	O
object	O
recognition	O
datasets	O
such	O
as	O
Oxford	O
Flower	O
Dataset	O
102	O
.	O
</s>
