Thesis - Instituto de Telecomunicações

122 CHAPTER 6. APPLICATIONS AND RESULTS10 in a dense matrix of numbers (see appendix B for a detailed description of the test). Theconcentration test was selected given that it was the one that produced more EDA eventsin all users. For all the results with EDA standalone classification we used half the data fortraining and half the data for classification.In the fusion experiments, we created a synthetic data source with the same number ofclasses. The data model was a multimodal normal N(µ, Σ) with µ i =[µ 1 , ··· ,µ nc ] whereµ j = 1 if j = i and µ j = 0 if j ≠ i otherwise (i is the class/user number). Σ is a diagonalmatrix with σ in each diagonal element. This model creates a class space where the classmeans are equally spaced from each other, providing a classification error that is distributedamong all the classes. For this model we just need to define the scalar σ that controls thedata separation. We used a σ that provided a base error for the synthetic classifier equalto 0.071.6.2.2 Feature AnalysisWe used only one of the extracted features, the one that provided the best classificationresults, namely the event amplitude. This selection was done empirically, and in this casewe skipped the automatic features selection step. Observing the data, we noticed that thefeature skewness for every user was 2.81±1.1 (mean value for all users). This gives groundto assume that the normal model does not fit the collected data well. Empirically, weobserved that taking the logarithm of the feature presented data with a distribution nearto the normal PDF (when measured, the skew of the transformed features, the mean valuewas -0.17 (± 0.42)). With these results we decided to apply the log transformation to thedata.In sequential classification, the sequence was sampled from the testing set. We allowedrepetition in the sampling process.The collected data is depicted in figure 6.4. For each user we present 125 samples. Avertical line separates events belonging to different users. For visualization purposes theusers are ordered by the mean value of the feature. We simplify this view in the error barplot of figure 6.5.Figure 6.6 presents the probability density functions of the SCR events log amplitudeof the EDA signal. We observe the overlap of several users that gives rise to the high error