Thesis - Instituto de Telecomunicações

5.4. UNCERTAINTY BASED CLASSIFICATION AND CLASSIFIER FUSION 111product rule for classifier fusion (see equation 5.22).p f (w i |x, y) = p c 1(w i |x)p c2 (w i |y). (5.22)p(w i )Figure 5.11: Diagram of the fusion of two classifiers, one based on a soft-biometric trait andthe other based on a hard-biometric trait.Generalization leads to the specification the classification fusion decision rule, by replacingp cj (w i |x j ) with g u i (x j), as given in equation 5.19. The decision rule for the 2 classifiersis:⎧⎨ true if gi u Accept(x, y ∈ w i )=(x)gu i (y) 1p(w i ) >λ⎩ false otherwise(5.23)The proposed classifier is schematically described in algorithm 3 for the two classifiersmodality. Generalization to m classifiers is straightforward.5.4.4 Related WorkWe proposed a new classification scheme integrating th information form the classificationerror probability in a uncertainty based reject option.This error probability value has already been used to create a reject option classifier,where a new pseudo-class is created, and used as a reject class [91]. If max i g i (x)