# Concept Drift Detection Based on Deep Neural Networks and Autoencoders
## 4 Experiment
### Experiment Results and Analysis
For example, in AGR_a and SEA_g, despite not achieving the best results on datasets like Sine_a, it ensures that a valid output is detected within each effective detection range. In cases where optimal performance is not achieved, this may be due to one or more detection instances failing to produce an output or providing an unsatisfactory result. Figure 8: Average rank of synthetic data with multiple drifts based on the Bonferroni–Dunn test. Figure 9: Different algorithms’ comparison on EDDR metrics of synthetic data with multiple drifts. Tables 8 and 9 present the \(FEDP\) and \(EDDR\) outputs for the detection algorithm on real-world datasets with single and multiple drifts, respectively. Due to the varying sizes of the real datasets, we set the drift point outputs to 100,000 for algorithms that fail to detect drift, leading to larger values in Table 8. The best outcomes are highlighted in bold. From these tables, it can be observed that the DNN+AE-DD algorithm demonstrates strong overall performance on both single-drift and multiple-drift real-world datasets. While our algorithm does not always achieve optimal performance on certain datasets, its results are only slightly below the best cases. These findings further validate the effectiveness of the DNN+AE-DD algorithm in detecting concept drift in streaming data. In Figure 10, the computed value of \(\mathcal{T}_{F}\) is 3.28. When \(k=9\) and \(N=6\), \(\mathcal{T}_{F}\) follows an F-distribution with degrees of freedom (8, 40), with a critical value of 2.18. This result leads to the rejection of the null hypothesis that \"all algorithms perform equally\". At a confidence level of \(\alpha=0.05\), the critical value \(q_{\alpha}\) is 2.724, yielding a critical difference (\(CD\)) value of 4.31. As illustrated in the figure, the proposed algorithm demonstrates significantly better performance in terms of delay detection compared to the DDM_NB, DDM_HT, ADWIN_NB, and ADWIN_HT. In Figure 11, the computed value of \(\mathcal{T}_{F}\) is 6.62. When \(k=9\) and \(N=5\), \(\mathcal{T}_{F}\) follows an F-distribution with degrees of freedom (8,32), with a critical value of 2.244. This result also leads to the rejection of the null hypothesis that \"all algorithms perform equally\". At a confidence level of \(\alpha=0.05\), the critical value \(q_{\alpha}\) is 2.724, yielding a \(CD\) value of 4.72. As shown in the figure, the proposed algorithm significantly outperforms the DDM_HT, ADWIN_NB, and ADWIN_HT in terms of the effective detection range. \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{2-9}  & & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** \\ \hline Weather & **1.0 (I)** & 93,946.00 & 95,946.00 & 64.00 (4) & 93017.20 (7) & 23.00 (2) & 28.00 (3) & 685.84 (6) & 579.60 (5) \\ Electricity & **2.0 (I)** & 4.00 (2) & 69,00.0(6) & 9.00 (3) & 56.00 (5) & 105.00 (7) & 53.00 (4) & 126.00 (8) & 158.00 (9) \\ Usenet1 & **1.08 (I)** & 49,923.99 (8) & 49,907.98 (7) & 344.51 (5) & 343.05 (4) & 247.00 (2.5) & 247.00 (2.5) & 68,722.21 (9) & 7940.50 (6) \\ Usenet2 & **4.3 (I)** & 415.99 (6) & 416.53 (7) & 344.79 (3) & 332.96 (2) & 400.00 (4.5) & 400.00 (4.5) & 99,490.00 (8) & 99,499.00 (8) \\ Email data & **8.35 (I)** & 99,499.00 (8) & 49,913.00 (5) & 293.72 (3) & 286.95 (2) & 99,499.00 (8) & 99,499.00 (8) & 27,106.43 (4) & 75,675.40 (6) \\ NSI-KDD & **34.37 (I)** & 2725.05 (5) & 451.76 (2) & 86,539.01 (7) & 86,538.48 (6) & 87,403.0 (8.5) & 87,403.0 (8.5) & 995.14 (4) & 453.38 (3) \\ \hline Average & \multirow{2}{*}{**1.0**} & \multirow{2}{*}{6.25} & \multirow{2}{*}{5.92} & \multirow{2}{*}{4.17} & \multirow{2}{*}{4.33} & \multirow{2}{*}{5.42} & \multirow{2}{*}{5.08} & \multirow{2}{*}{6.58} & \multirow{2}{*}{6.25} \\ rank & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: FEDP comparison of real-world data with single drift.