<s>
In	O
machine	O
learning	O
,	O
a	O
Ranking	B-Algorithm
SVM	I-Algorithm
is	O
a	O
variant	O
of	O
the	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
algorithm	O
,	O
which	O
is	O
used	O
to	O
solve	O
certain	O
ranking	O
problems	O
(	O
via	O
learning	O
to	O
rank	O
)	O
.	O
</s>
<s>
The	O
ranking	B-Algorithm
SVM	I-Algorithm
algorithm	O
was	O
published	O
by	O
Thorsten	O
Joachims	O
in	O
2002	O
.	O
</s>
<s>
The	O
original	O
purpose	O
of	O
the	O
algorithm	O
was	O
to	O
improve	O
the	O
performance	O
of	O
an	O
internet	B-Application
search	I-Application
engine	I-Application
.	O
</s>
<s>
However	O
,	O
it	O
was	O
found	O
that	O
Ranking	B-Algorithm
SVM	I-Algorithm
also	O
can	O
be	O
used	O
to	O
solve	O
other	O
problems	O
such	O
as	O
Rank	B-General_Concept
SIFT	I-General_Concept
.	O
</s>
<s>
The	O
Ranking	B-Algorithm
SVM	I-Algorithm
algorithm	O
is	O
a	O
learning	O
retrieval	O
function	O
that	O
employs	O
pair-wise	O
ranking	O
methods	O
to	O
adaptively	O
sort	O
results	O
based	O
on	O
how	O
'	O
relevant	O
 '	O
they	O
are	O
for	O
a	O
specific	O
query	B-Library
.	O
</s>
<s>
The	O
Ranking	B-Algorithm
SVM	I-Algorithm
function	O
uses	O
a	O
mapping	O
function	O
to	O
describe	O
the	O
match	O
between	O
a	O
search	O
query	B-Library
and	O
the	O
features	O
of	O
each	O
of	O
the	O
possible	O
results	O
.	O
</s>
<s>
This	O
mapping	O
function	O
projects	O
each	O
data	O
pair	O
(	O
such	O
as	O
a	O
search	O
query	B-Library
and	O
clicked	O
web-page	O
,	O
for	O
example	O
)	O
onto	O
a	O
feature	O
space	O
.	O
</s>
<s>
These	O
features	O
are	O
combined	O
with	O
the	O
corresponding	O
click-through	O
data	O
(	O
which	O
can	O
act	O
as	O
a	O
proxy	O
for	O
how	O
relevant	O
a	O
page	O
is	O
for	O
a	O
specific	O
query	B-Library
)	O
and	O
can	O
then	O
be	O
used	O
as	O
the	O
training	O
data	O
for	O
the	O
Ranking	B-Algorithm
SVM	I-Algorithm
algorithm	O
.	O
</s>
<s>
Generally	O
,	O
Ranking	B-Algorithm
SVM	I-Algorithm
includes	O
three	O
steps	O
in	O
the	O
training	O
period	O
:	O
</s>
<s>
It	O
maps	O
the	O
similarities	O
between	O
queries	B-Library
and	O
the	O
clicked	O
pages	O
onto	O
a	O
certain	O
feature	O
space	O
.	O
</s>
<s>
It	O
forms	O
an	O
optimization	O
problem	O
which	O
is	O
similar	O
to	O
a	O
standard	O
SVM	B-Algorithm
classification	O
and	O
solves	O
this	O
problem	O
with	O
the	O
regular	O
SVM	B-Algorithm
solver	O
.	O
</s>
<s>
Kendall	B-General_Concept
's	I-General_Concept
Tau	I-General_Concept
also	O
refers	O
to	O
Kendall	B-General_Concept
tau	I-General_Concept
rank	I-General_Concept
correlation	I-General_Concept
coefficient	I-General_Concept
,	O
which	O
is	O
commonly	O
used	O
to	O
compare	O
two	O
ranking	O
methods	O
for	O
the	O
same	O
data	O
set	O
.	O
</s>
<s>
Suppose	O
and	O
are	O
two	O
ranking	O
method	O
applied	O
to	O
data	O
set	O
,	O
the	O
Kendall	B-General_Concept
's	I-General_Concept
Tau	I-General_Concept
between	O
and	O
can	O
be	O
represented	O
as	O
follows	O
:	O
</s>
<s>
Information	B-Library
retrieval	I-Library
quality	O
is	O
usually	O
evaluated	O
by	O
the	O
following	O
three	O
measurements	O
:	O
</s>
<s>
For	O
a	O
specific	O
query	B-Library
to	O
a	O
database	O
,	O
let	O
be	O
the	O
set	O
of	O
relevant	O
information	O
elements	O
in	O
the	O
database	O
and	O
be	O
the	O
set	O
of	O
the	O
retrieved	O
information	O
elements	O
.	O
</s>
<s>
Suppose	O
is	O
the	O
element	O
of	O
a	O
training	O
data	O
set	O
,	O
where	O
is	O
the	O
feature	B-Algorithm
vector	I-Algorithm
and	O
is	O
the	O
label	O
(	O
which	O
classifies	O
the	O
category	O
of	O
)	O
.	O
</s>
<s>
A	O
typical	O
SVM	B-Algorithm
classifier	O
for	O
such	O
data	O
set	O
can	O
be	O
defined	O
as	O
the	O
solution	O
of	O
the	O
following	O
optimization	O
problem	O
.	O
</s>
<s>
The	O
solution	O
of	O
the	O
above	O
optimization	O
problem	O
can	O
be	O
represented	O
as	O
a	O
linear	O
combination	O
of	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
s	O
.	O
</s>
<s>
Let	O
be	O
the	O
Kendall	B-General_Concept
's	I-General_Concept
tau	I-General_Concept
between	O
expected	O
ranking	O
method	O
and	O
proposed	O
method	O
,	O
it	O
can	O
be	O
proved	O
that	O
maximizing	O
helps	O
to	O
minimize	O
the	O
lower	O
bound	O
of	O
the	O
Average	O
Precision	O
of	O
.	O
</s>
<s>
where	O
is	O
the	O
statistical	O
distribution	O
of	O
to	O
certain	O
query	B-Library
.	O
</s>
<s>
queries	B-Library
are	O
applied	O
to	O
a	O
database	O
and	O
each	O
query	B-Library
corresponds	O
to	O
a	O
ranking	O
method	O
.	O
</s>
<s>
Each	O
element	O
contains	O
a	O
query	B-Library
and	O
the	O
corresponding	O
ranking	O
method	O
.	O
</s>
<s>
A	O
mapping	O
function	O
is	O
required	O
to	O
map	O
each	O
query	B-Library
and	O
the	O
element	O
of	O
database	O
to	O
a	O
feature	O
space	O
.	O
</s>
<s>
Then	O
the	O
ranking	O
problem	O
can	O
be	O
translated	O
to	O
the	O
following	O
SVM	B-Algorithm
classification	O
problem	O
.	O
</s>
<s>
Note	O
that	O
one	O
ranking	O
method	O
corresponds	O
to	O
one	O
query	B-Library
.	O
</s>
<s>
The	O
above	O
optimization	O
problem	O
is	O
identical	O
to	O
the	O
classical	O
SVM	B-Algorithm
classification	O
problem	O
,	O
which	O
is	O
the	O
reason	O
why	O
this	O
algorithm	O
is	O
called	O
Ranking-SVM	O
.	O
</s>
<s>
For	O
new	O
query	B-Library
,	O
the	O
retrieval	O
function	O
first	O
projects	O
all	O
elements	O
of	O
the	O
database	O
to	O
the	O
feature	O
space	O
.	O
</s>
<s>
And	O
the	O
rank	O
of	O
each	O
feature	O
point	O
is	O
the	O
rank	O
of	O
the	O
corresponding	O
element	O
of	O
database	O
for	O
the	O
query	B-Library
.	O
</s>
<s>
Ranking	B-Algorithm
SVM	I-Algorithm
can	O
be	O
applied	O
to	O
rank	O
the	O
pages	O
according	O
to	O
the	O
query	B-Library
.	O
</s>
<s>
Query	B-Library
.	O
</s>
<s>
The	O
combination	O
of	O
2	O
and	O
3	O
cannot	O
provide	O
full	O
training	O
data	O
order	O
which	O
is	O
needed	O
to	O
apply	O
the	O
full	O
SVM	B-Algorithm
algorithm	O
.	O
</s>
<s>
So	O
the	O
condition	O
of	O
optimization	O
problem	O
becomes	O
more	O
relax	O
compared	O
with	O
the	O
original	O
Ranking-SVM	O
.	O
</s>
