Thesis - Instituto de Telecomunicações

5.4. UNCERTAINTY BASED CLASSIFICATION AND CLASSIFIER FUSION 1091.01.01.01.00.80.80.80.80.60.60.60.6pe(x)0.40.40.40.40.20.20.20.20.00 5 10 15 20x=-30.00.00 5 10 15 20x=-20.00 5 10 15 20x=-10 5 10 15 20x=0Figure 5.9: Distribution of ˆp(x|w i ) at points x =[−3, −2, −1, 0].Figure 5.10: Variance of ˆp(x|w i ).to the typical rejection option using the variance of ĝ i (x ∗ ) to establish a new rejection rule.We define g u i (x∗ ) as:g u i (x∗ )=k[ĝ i (x ∗ )+w std(ĝ i (x ∗ ))], (5.19)where (·) denotes the mean value, and k is a normalizing factor to guarantee that ∑ n ci=1 gu i (x∗ )=1; w weights the contribution of the standard deviation of ĝ i (x ∗ ) in the modified discriminantfunction.When w → 0, g u i (x∗ ) → g i (x ∗ ), corresponding to the standard discriminant function.When w →∞, g u i (x∗ ) → std(ĝ i (x ∗ )). For our tests we selected w = 1; The new discriminantfunctions add a class dependent value that will balance the uncertainty estimated for theclassification among all the classes.The proposed rejection rule is expressed by