Master Thesis - Department of Computer Science

can be organized as a matrix called decision profile (DP):
⎡
⎤
⎢ d1,1(x)
⎢ . . .
⎢
DP (x) = ⎢ di,1(x)
⎢ . . .
⎣
dL,1(x)
. . .
. . .
. . .
. . .
. . .
d1,j(x)
. . .
di,j(x)
. . .
dL,j(x)
. . .
. . .
. . .
. . .
. . .
d1,C(x) ⎥
. . . ⎥
di,C(x) ⎥
. . . ⎥
⎦
dL,C(x)
We denote i th row of the above matrix as Di(x) = [di,1(x), ....., di,C(x)], where di,j(x)
is the degree of support given by classifier Di to the hypothesis that x belongs to
class j. Di(x) is the response vector of classifier Di for a sample x. The task of any
combination rule is to construct ˜ D(x), the fused output of L classifiers as:
˜D(x) = F(D1(x), ......, DL(x)) (2.21)
Some fusion techniques known as class-conscious [68], do column-wise class-by-class
operation on DP(x) matrix to obtain ˜ D(x). Example of this type of fusion techniques
are: sum, product, min, max, etc [60]. Another fusion approach known as class-
indifferent [68], use entire DP(x) to calculate ˜ D(x).
Class-conscious Methods
Given DP (x), class-conscious methods operate class-wise on each column of DP (x).
The architecture of class-conscious methods is demonstrated in Fig. 2.12.
• Sum Rule: Sum Rule computes the soft class label vectors using
˜d j (x) =
L�
di,j, j = 1, ...., C (2.22)
i=1
• Product Rule: Product Rule computes the soft class label vectors as
˜d j (x) =
L�
di,j, j = 1, ...., C (2.23)
• Min Rule: Min Rule computes the soft class label vectors using
i=1
˜d j (x) = min(d1,j, d2,j, ....., dL,j), j = 1, ...., C (2.24)
• Max Rule: Max Rule computes the soft class label vectors using
˜d j (x) = max(d1,j, d2,j, ....., dL,j), j = 1, ...., C (2.25)
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