Digital Signal Processing Reference
In-Depth Information
DF
=
N
00
/
N
.
(4)
ik
,
4) Correlation Coefficient
[12]
: The correlation between two base classifier outputs is
defined as follows
ρ
=
(
NN NN
11
00
−
01
10
) /
(
NNNNNNNN
11
+
10
)(
01
+
00
)(
11
+
01
)(
10
+
00
)
.
(5)
ik
,
5) Entropy Measure: The measure is defined as
1
N
1
E
=
min{ (
l
z
),
L
−
l
(
z
)}
,
(6)
j
j
NLL
=
(
−
/ 2 )
j
1
where (
l
z
denotes the number of classifiers that correctly recognize
z
.
6) Kohavi-Wolpert Variance: The measure is derived from the decomposition formula
proposed in [14] as
)
j
1
N
z
KW
=
l
( (
L
−
l
( )
z
.
(7)
2
j
j
NL
j
=
1
7) Measure of Difficulty [1]: Let
X
be a random variable taking values in
{0
LL
and denoting the proportion of classifiers that correctly classify an
object drawn randomly from the distribution of the problem. The measure of difficul-
ty is defined as the variance of
X
. Diverse teams of base classifiers will have small
variance.
,1
,
,1}
θ =
var(
X
)
(8)
8) Generalized Measure [15]: Let
Y
be a random variable denoting the proportion of
classifiers out of
L
that fail on a randomly drawn object
n
x
∈ℜ
. Denote by
p
the
probability that
Yi L
pi
the probability that
i
randomly chosen clas-
sifiers will fail on a randomly chosen
x
. The generalized diversity measure is
=
and by
( )
GD
=−
1( ) /
p
p
( )
,
(9)
L
i
L
ii
−
1
and
where
p
(1)
=
p
p
(2)
=
p
.
i
i
L
LL
(
−
)
i
=
1
i
=
1
9) Coincident Fault Diversity
[15]: This measure is a modification of the generalized
diversity measure.
0
p
=
1
0
CFD
=
.
(10)
1
Li
pp
pL
=
L
−
<
1
i
0
1
−
−
1
i
1
0
