Thesis - Instituto de Telecomunicações

6.2. SYMPATHETIC DYNAMICS BIOMETRICS 129verify the fusion tools that we designed to create a fusion classifier, which improves the firsthard-biometric based classifier.As base fusion rule we used the multiplication of g i for each classifier, referred to as theproduct rule. We also tested the uncertainty based classification fusion with the sum rule,but results were always worse than the ones obtained with the product rule.In the following examples we just compare the product rule with the product rule basedon the bootstrap discriminant functions gi u(x∗ ) (see equation 5.19).The evolution of the equal error rate for different training sample sizes is depictedin figure 6.12. We generated the data from 10 runs of the fusion algorithm for differenttraining set sizes (we report the number of samples in the training set per user). Thenumber of bootstrap samples was set to 100. We used a sequence size of 25 sequentialtesting samples. We observed that with a small testing sample set the direct fusion willgenerate more error than the synthetic data classifier alone. The uncertainty based rejectoption will always improve classifications, and for small training sets will outperform thenormal fusion. When more training data is available both classification fusion techniqueshave similar performance.The number of bootstrap samples also influences the performance of the uncertaintybased classifier fusion. We tested the fusion classification with a training set of 10 samplesper user and for a sequence length of 25 samples. We then ran the algorithm for differentbootstrap sample sizes. We observe an improvement in the equal error rate that stabilizeswith ≈ 20 bootstrap samples (see figure 6.13).The obtained results are of relevance for highly overlapping data as the EDA signal.The uncertainty based approach we developed, introduces significant improvements bothfor stand alone rejection and for classifier fusion.