Master Thesis - Department of Computer Science

Class-indifferent Methods
• Decision Template (DT): Let Z = {z1 1 , z1 2 , ...z1 M , z2 1 ..., z2 M , ....., zC M }, zi j ∈ Rn
be the crisply labeled validation set which is a disjoint from training and testing
set. M is the number of validation samples per class. DP Z is the set of DP’s
corresponding to the samples in Z. Hence DP Z is a 3-dimensional matrix of
size L × C × N where N = M ∗ C.
1. Decision template DTi of class i is the L × C matrix and is computed
from DP Z as
DTi = 1
M
i∗M �
j=(i−1)∗M+1
DP Z
.,.,j, i = 1, ...., C (2.26)
The decision template DTi for class i is the average of the decision profiles
of the elements in the validation set Z labeled as class i.
2. When a test vector, x ∈ R n is submitted for classification, DP (x) is
matched with DTi, i = 1, ..., C and produces the soft class label vector
˜d j (x) = S(DTi, DP (x)), i = 1, ....., C. (2.27)
where S is a function which returns similarity measure between it’s ar-
guments. It can be euclidean distance or any fuzzy set similarity measure.
• Dempster-Shafer Combination (DS): Dempster-Shafer algorithm performs
the following steps:
1. Let DT i j denotes the i th row of the decision template for class j. Calculate
the proximity Φ between DT i j and Di(x) for every class j=1,....,C, and for
every classifier i=1,...,L. The proximity [103] is calculated using
where � ∗ � is any matrix norm.
Φj,i(x) = (1 + �DT i j − Di(x)�2 ) −1
�Ck=1 (1 + �DT i k − Di(x)�2 , (2.28)
) −1
2. For each class, j=1,....,C and for every classifier, i=1,...., L, calculate
belief degrees
bj(Di(x)) =
Φj,i(x) �
k�=j(1 − Φk,i(x))
1 − Φj,i(x)[1 − �
, (2.29)
k�=j(1 − Φk,i(x))]
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