# Concept Drift Detection Based on Deep Neural Networks and Autoencoders
## 4 Experiment
### Experiment Results and Analysis

Table 6: FEDP on synthetic data with single drift. Figure 6: Average rank of synthetic data with single drift based on the Bonferroni–Dunn test. this transition, which can cause detection delays. As a result, the detection performance of the algorithm may vary across different datasets. For incremental drift data, the data in the transitional period do not belong strictly to either the new or old distribution, which allows the DNN+AE-DD to detect the drift with relatively shorter delay. The data in Table 7 show the performance of various algorithms on the \(EDDR\) metric for synthetic multi-drift data. An ideal result for this metric is a value close to 1.0, with the best results highlighted in bold. This metric illustrates that each drift detection algorithm has its optimal performance at specific moments, but overall, the method proposed in this paper performs well. A value of 0.0 in Table 7 may indicate that the current detector did not identify values within the valid detection range for a particular dataset. In such cases, the detector might have produced a result, but the detection outcome was suboptimal, or the detector might have failed to detect the occurrence of drift. Based on Equation (8), we obtain \(\mathcal{T}_{F}=3.80\). When \(k=9\) and \(N=7\), \(\mathcal{T}_{F}\) follows an F-distribution with degrees of freedom (8, 48), with a critical value of 2.138, leading \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multirow{2}{*}{**DNN+AE-DD**} & \multicolumn{2}{c}{**DDM**} & \multicolumn{2}{c}{**EDDM**} & \multicolumn{2}{c}{**HDDM\_W**} & \multicolumn{2}{c}{**ADWIN**} \\ \cline{2-10}  & & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** \\ \hline ACR\_a & **0.98 (I)** & 0.00 (6.5) & 0.00 (6.5) & 0.00 (6.5) & 0.04 (3) & 0.00 (6.5) & 0.00 (6.5) & 0.00 (6.5) & 0.09 (2) \\ SE\_a & **0.87 (I)** & 0.00 (6) & 0.00 (6) & 0.00 (6) & 0.00 (6) & 0.00 (6) & 0.00 (6) & 0.01 (2) & 0.00 (6) \\ Sine\_a & 0.86 (3) & 0.01 (6.5) & 0.00 (8.5) & 0.01 (6.5) & 0.00 (8.5) & 0.67 (4.5) & **1.00 (1.5)** & **1.00 (1.5)** & 0.67 (4.5) \\ ACR\_g & **0.96 (I)** & 0.0 (8) & 0.0 (8) & 0.11 (5) & 0.17 (4) & 0.22 (3) & 0.44 (2) & 0.06 (6) & 0.0 (8) \\ SE\_g & **0.83 (I)** & 0.01 (5.5) & 0.00 (8) & 0.67 (2) & 0.01 (5.5) & 0.00 (8) & 0.00 (8) & 0.04 (4) & 0.06 (3) \\ Sine\_g & 0.86 (3) & 0.5 (7) & 0.67 (5) & 0.00 (9) & 0.33 (8) & 0.67 (5) & 0.67 (5) & **1.00 (1.5)** & **1.00 (1.5)** \\ Mixed\_A & 0.98 (4) & 0.00 (8.5) & 0.25 (7) & 0.00 (8.5) & 0.38 (6) & 0.50 (5) & **1.00 (2)** & **1.00 (2)** & **1.00 (2)** \\ \hline Average rank & **2.0** & 6.86 & 7.0 & 6.21 & 5.86 & 5.43 & 4.43 & 3.36 & 3.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: EDDR on synthetic data with multiple drifts. Figure 7: Different algorithms’ comparsion on FEDP metrics of synthetic data with single drift. us to reject the hypothesis that \"all algorithms perform equally\". At a confidence level of \(\alpha=0.05\), \(q_{\alpha}=2.724\), yielding a critical difference (\(CD\)) value of 3.99. The statistical results are shown in Figure 8. As seen in the figure, the proposed algorithm significantly outperforms DDM_NB and DDM_HT in terms of effective detection metrics. In Figure 9, the different colored bars represent different effective detection ranges. SEA and Sine each have three effective detection ranges, corresponding to three colored bars, while mixed has four effective detection ranges and AGR has nine effective detection ranges. The results in Table 7 represent the average values for each effective detection range (with an average value of 1.0 only when all bars have a value of 1.0). Figure 9 presents detailed results for each effective detection range. From the figure, when facing multiple abrupt/gradual drift datasets, we can observe that although the DNN+AE-DD does not guarantee the best performance across all datasets, it performs well on most abrupt/gradual drift datasets.