<s>
In	O
statistical	B-General_Concept
classification	I-General_Concept
,	O
the	O
Fisher	B-Algorithm
kernel	I-Algorithm
,	O
named	O
after	O
Ronald	O
Fisher	O
,	O
is	O
a	O
function	O
that	O
measures	O
the	O
similarity	O
of	O
two	O
objects	O
on	O
the	O
basis	O
of	O
sets	O
of	O
measurements	O
for	O
each	O
object	O
and	O
a	O
statistical	O
model	O
.	O
</s>
<s>
In	O
a	O
classification	O
procedure	O
,	O
the	O
class	O
for	O
a	O
new	O
object	O
(	O
whose	O
real	O
class	O
is	O
unknown	O
)	O
can	O
be	O
estimated	O
by	O
minimising	O
,	O
across	O
classes	O
,	O
an	O
average	O
of	O
the	O
Fisher	B-Algorithm
kernel	I-Algorithm
distance	O
from	O
the	O
new	O
object	O
to	O
each	O
known	O
member	O
of	O
the	O
given	O
class	O
.	O
</s>
<s>
The	O
Fisher	B-Algorithm
kernel	I-Algorithm
was	O
introduced	O
in	O
1998	O
.	O
</s>
<s>
It	O
combines	O
the	O
advantages	O
of	O
generative	O
statistical	O
models	O
(	O
like	O
the	O
hidden	O
Markov	O
model	O
)	O
and	O
those	O
of	O
discriminative	B-General_Concept
methods	I-General_Concept
(	O
like	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
)	O
:	O
</s>
<s>
discriminative	B-General_Concept
methods	I-General_Concept
can	O
have	O
flexible	O
criteria	O
and	O
yield	O
better	O
results	O
.	O
</s>
<s>
The	O
Fisher	B-Algorithm
kernel	I-Algorithm
is	O
the	O
kernel	O
for	O
a	O
generative	O
probabilistic	O
model	O
.	O
</s>
<s>
Fisher	B-Algorithm
kernels	I-Algorithm
exist	O
for	O
numerous	O
models	O
,	O
notably	O
tf	O
–	O
idf	O
,	O
Naive	B-General_Concept
Bayes	I-General_Concept
and	O
probabilistic	B-General_Concept
latent	I-General_Concept
semantic	I-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
The	O
Fisher	B-Algorithm
kernel	I-Algorithm
can	O
also	O
be	O
applied	O
to	O
image	O
representation	O
for	O
classification	O
or	O
retrieval	O
problems	O
.	O
</s>
<s>
Currently	O
,	O
the	O
most	O
popular	O
bag-of-visual-words	B-General_Concept
representation	O
suffers	O
from	O
sparsity	O
and	O
high	O
dimensionality	O
.	O
</s>
<s>
The	O
Fisher	B-Algorithm
kernel	I-Algorithm
can	O
result	O
in	O
a	O
compact	O
and	O
dense	O
representation	O
,	O
which	O
is	O
more	O
desirable	O
for	O
image	O
classification	O
and	O
retrieval	O
problems	O
.	O
</s>
<s>
The	O
Fisher	O
Vector	O
(	O
FV	O
)	O
,	O
a	O
special	O
,	O
approximate	O
,	O
and	O
improved	O
case	O
of	O
the	O
general	O
Fisher	B-Algorithm
kernel	I-Algorithm
,	O
is	O
an	O
image	O
representation	O
obtained	O
by	O
pooling	O
local	O
image	B-Algorithm
features	I-Algorithm
.	O
</s>
<s>
In	O
a	O
systematic	O
comparison	O
,	O
FV	O
outperformed	O
all	O
compared	O
encoding	O
methods	O
(	O
Bag	B-General_Concept
of	I-General_Concept
Visual	I-General_Concept
Words	I-General_Concept
(	O
BoW	O
)	O
,	O
Kernel	O
Codebook	O
encoding	O
(	O
KCB	O
)	O
,	O
Locality	O
Constrained	O
Linear	O
Coding	O
(	O
LLC	O
)	O
,	O
Vector	O
of	O
Locally	O
Aggregated	O
Descriptors	O
(	O
VLAD	O
)	O
)	O
showing	O
that	O
the	O
encoding	O
of	O
second	O
order	O
information	O
(	O
aka	O
codeword	O
covariances	O
)	O
indeed	O
benefits	O
classification	O
performance	O
.	O
</s>
