Biomedical Engineering Reference
In-Depth Information
Table 2.
Adaboost Algorithm
2
m
,
2
l
1
[Initialization]
w
1
,i
=
for
c
i
=
{−
1
,
1
}
respectively.
Step 1.
Normalize weights
w
t,i
j
=1
w
t,i
←
w
t,i
Step 2.
For each dimension
j
, train a classifier,
h
j
which is restricted
to using that single random variable.
The
error
is
evaluated with respect
to
w
t
,
j
=
i
w
i
|
h
j
(
x
i
)
−
c
i
|
.
Step 3.
Choose the classifier,
h
t
with the lowest error
t
.
Step 4.
Update the weights:
w
t
+1
,i
=
w
t,i
β
e
i
t
where
e
i
=1for each well-classified feature and
e
i
=0other-
wise.
β
t
=
t
1
−
t
.
Step 5.
Calculate the parameter
α
t
=
−
log
(
β
t
).
Step 6.
t
=
t
+1.
If
t
≥
T
go to Step 1
The final
strong
classifier is:
1
c
r
=
t
=1
α
t
h
t
(
x
)
≥
0
h
(
x
)=
0
otherwise
where
c
r
is the confidence rate associated with the label.
learners is reduced, or increased otherwise. As a result, each classifier is centered
in the most difficult data up to that point.
Let the training set be composed by
N
pairs
is
the class of each multidimensional data point
x
i
. Let
w
t,i
be the weighting factor
at time
t
for data point
x
i
. Also, let
l
and
m
be the number of data points for each
class. The adaboost algorithm is described in the Table 2.
Parameter
α
t
is the weighting factor of each of the classifiers of the ensemble.
The loop ends whether the classification error of a the
weak
classifier is over 0.5;
{
x
i
,c
i
}
, where
c
i
=
{−
1
,
1
}
