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In-Depth Information
Algorithm 7.2
Learn
++
for nonstationary data stream with imbalanced class
distribution
Inputs:
1: timestamp:
t
2: current training data chunk:
S
(t)
={
(
x
1
,y
1
),...,(
x
m
,y
m
)
}
(t)
x
1
,...,
x
n
}
3: current data set under evaluation:
T
={
4: soft-typed base classifier:
L
/* a soft-typed base classifier outputs the likelihood
f
that an instance
x
belongs to each class
instead of a hard class label. */
5: hypotheses set
H
:
h
1
,...,h
t
−
1
}
/*
h
i
is the base hypothesis created at the data chunk with timestamp
i
*/
{
Procedure:
6:
for
t
:1
→
...
do
7:
(t)
(t)
,
N
(t)
S
→{
P
}
8:
repeat
M
(t)
←
SMOTE
(
P
(t)
)
9:
10:
h
t
←
L(
{
S
(t)
,
M
(t)
}
)
m
×
i
=
1
[[
h
t
(
x
i
)
=
y
i
]]
/* [[
c
]]
1
11:
ε
=
=
1
if and only if
cis
true
and 0 otherwise */
12:
until
ε<
0
.
5
13:
H
←{
H
,h
t
}
14:
W
←{}
15:
for
i
:1
→
t
do
ε
i
←
j
=
1
[[
h
i
(
x
j
)
16:
=
y
j
]]
/m
17:
w
i
←
log
((
1
−
ε
i
)/ε
i
)
18:
if
w
i
>
0
then
19:
W
←{
W
,w
i
}
20:
else
21:
W
←{
W
,
0
}
return
Composite hypothesis
h
(t)
(t)
22:
final
for predicting the class label of
T
is
H
×
W
, i.e.,
t
h
(t)
final
(
x
j
)
f
i
(
x
j
)
=
argmax
c
∈
Y
w
i
×
(7.3)
i
=
1
/*
f
i
(
x
j
)
is the
a posteriori
probability for
x
j
belonging to class
c
output by
h
i
.*/
created on the augmented data chunk to make predictions on the testing dataset.
The method of creating the ensemble classifiers is similar to the classic bag-
ging method [33] in that multiple hypotheses created on randomly permutated
sets are aggregated with uniform weights into a composite classifier. However,
considering the limited number of minority class examples available in training
data chunk, only the majority class set is randomly sampled without replace-
ment. This differs from classic bagging in that the sample sets have no overlaps
at all. Therefore, it is referred as
uncorrelated bagging
(UB) in the rest of this
chapter. The dataset that is used to create base hypothesis
h
contains exactly
the same minority examples and different majority class examples. In this way,
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