Proceedings of the 9th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED), University of Cambridge, UK, 2010, edited by L. A. Zadeh et al, pp 191 - 195 were aged from 40 to 45 weeks post-conception.

Each of these 6 groups contains around 100 patients.

The EEGs have been segmented in 10-s intervals to be represented by 72 attributes as spectral powers and their variances. We averaged the EEG segments of each patient to represent the patient by one data sample, so that the problem was represented by 686 data samples in 72 attribute space.

 For experiments we used the Bayesian averaging over DT models introduced in section 3 and described in our previous publications [12]. The BMA ran with the following settings. In a burn-in phase we collected 200,000 DTs, and in a post burnin phase 10,000 DTs. During the post burn-in phase each 7th model was collected to reduce the correlation between DT models. The minimal number of data samples allowed in DT nodes was 6. Proposal variance was 1.0, and probabilities of making moves of birth, death, change variable, and change threshold were set to 0.15, 0.15, 0.1, and 0.6, respectively. The performance and uncertainty of the DT ensemble collected in the post burn-in phase were evaluated within a 3-fold cross-validation and
±2V intervals.

 The BMA with the above settings has accepted around 0.13 of DT models in both phases. The DT size becomes stationary around 30 nodes soon after 10,000 samples of burn-in phase. The average performance was 27.4%, whilst the accuracy of classification by chance was 100/6 = 16.7%. The performance varied within 2V interval equal to 8.2%. The entropy of the DT ensemble was 478.3±15.8. According to the proposed technique, we estimated the importance of all the 72 attributes in terms of the posterior probabilities of using these attributes by the DT models collected in the post burn-in phase. The posterior probabilities of using the attributes ranged between 0.0 and 0.005. We then gradually increased the threshold value T from 0 at steps of 0.001 to 0.005 to define features as weak accordingly to the proposed strategy of feature selection. From Table 1, we can see that at threshold value 0.001 the average number of weak attributes, k, was 14, whilst at level 0.005 their number has increased to 31. Having found the weak attributes, we applied the proposed technique to refine the DT ensemble.

Table 1 shows the number of weak attributes, k, versus the threshold values, T, within a 3-fold crossvalidation. From Table 1 we can see that the performance P of the refined DT ensemble is slightly increased from 27.4 to 29.2 when the threshold is gradually increased from 0.0 to 0.005.

At the same time the uncertainty in decisions is decreased from 478.4 to 469.0 in terms of entropy E
of the ensemble. For comparison, we applied a technique of discarding the same weak attributes and then reran the BMA on the data reduced in their dimensionality.

 From Table 1 we can see that the BMA performance has slightly increased from 27.4 to 29.0 when 23 weak attributes were discarded. The discarding of 31 attribute has resulted in a decrease in the ensemble entropy from 478.3 to 463.6.

Overall, the both techniques are shown to provide the comparable performance and ensemble entropy. However, the technique of discarding attributes has shown to tend to perform in a larger variation.

Within this technique for each threshold value it is required to retrain DT ensemble on the data of a new dimensionality.

| Table 1. Performance (P) and entropy (E) of the techniques versus threshold values (T) within 3-fold cross-validation. T k Proposed technique Technique of discarding attributes P, % E P, % E 0.001 14 27.5±8.4 478.4±15.8 28.7±9.6 469.0±13.7 0.002 18 27.8±9.0 477.7±16.4 25.8±1.7 475.7±16.7 0.003 23 28.7±8.2 475.7±15.3 29.0±8.5 474.1±33.9 0.004 28 28.9±7.6 471.2±10.3 28.4±1.8 472.4±12.0 0.005 31 29.2±7.9 469.0±11.9 27.3±6.5 463.6±26.3   |
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 Fig 1 shows the distributions of performances

![0_image_0.png](0_image_0.png) calculated for the original and refined DT
ensembles. According to the proposed method, the refinement has been obtained by discarding those DTs which use 26 weak attributes. We can see that the size of the refined ensemble becomes significantly smaller. Most of the DTs with performance above 32.0% have been kept, whilst most of the DTs with performance below 24.0% have been discarded from the refined ensemble.