Furthermore, based on the feedback from several system specialists, who mention that the online data set is totally independent from the training data set and contains some different system states that may cause a drift resp. shift of the underlying data distribution, gradual forgetting (as outlined in section 5.4.3) was carried out during the evolution of the models on the whole online data. The results are reported in the last-butone row of Table 5.1 and show a signi cant increase in the validation measures; especially, the number of big too low errors could be reduced by almost one-third. Please also note that for all the mentioned results the heuristic regularization approach was implicitly applied in FLEXFIS; otherwise, the MAE suffers drastically. (See the last line in Table 5.1). This means that regularization is quite necessary in order to achieve reasonable results at all. In Figure 5.11, the evolution of the number of rules is shown for both variants, where the initial number of rules (5.21) is obtained from the initial batch training and cross-validation procedure performed on the training data; four additional rules have emerged during the online phase, which lead to signi cantly better results, as shown in Table 5.1.
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