Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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Class-indifferent Methods<br />
• Decision Template (DT): Let Z = {z1 1 , z1 2 , ...z1 M , z2 1 ..., z2 M , ....., zC M }, zi j ∈ Rn<br />
be the crisply labeled validation set which is a disjoint from training and testing<br />
set. M is the number <strong>of</strong> validation samples per class. DP Z is the set <strong>of</strong> DP’s<br />
corresponding to the samples in Z. Hence DP Z is a 3-dimensional matrix <strong>of</strong><br />
size L × C × N where N = M ∗ C.<br />
1. Decision template DTi <strong>of</strong> class i is the L × C matrix and is computed<br />
from DP Z as<br />
DTi = 1<br />
M<br />
i∗M �<br />
j=(i−1)∗M+1<br />
DP Z<br />
.,.,j, i = 1, ...., C (2.26)<br />
The decision template DTi for class i is the average <strong>of</strong> the decision pr<strong>of</strong>iles<br />
<strong>of</strong> the elements in the validation set Z labeled as class i.<br />
2. When a test vector, x ∈ R n is submitted for classification, DP (x) is<br />
matched with DTi, i = 1, ..., C and produces the s<strong>of</strong>t class label vector<br />
˜d j (x) = S(DTi, DP (x)), i = 1, ....., C. (2.27)<br />
where S is a function which returns similarity measure between it’s ar-<br />
guments. It can be euclidean distance or any fuzzy set similarity measure.<br />
• Dempster-Shafer Combination (DS): Dempster-Shafer algorithm performs<br />
the following steps:<br />
1. Let DT i j denotes the i th row <strong>of</strong> the decision template for class j. Calculate<br />
the proximity Φ between DT i j and Di(x) for every class j=1,....,C, and for<br />
every classifier i=1,...,L. The proximity [103] is calculated using<br />
where � ∗ � is any matrix norm.<br />
Φj,i(x) = (1 + �DT i j − Di(x)�2 ) −1<br />
�Ck=1 (1 + �DT i k − Di(x)�2 , (2.28)<br />
) −1<br />
2. For each class, j=1,....,C and for every classifier, i=1,...., L, calculate<br />
belief degrees<br />
bj(Di(x)) =<br />
Φj,i(x) �<br />
k�=j(1 − Φk,i(x))<br />
1 − Φj,i(x)[1 − �<br />
, (2.29)<br />
k�=j(1 − Φk,i(x))]<br />
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