# Concept Drift Detection Based on Deep Neural Networks and Autoencoders
## 4 Experiment
### Experiment Results and Analysis
When \(k=9\) and \(N=9\), \(\mathcal{T}_{F}\) follows an F-distribution with degrees of freedom (8, 64), with a critical value of 2.087. Therefore, we reject the hypothesis that all algorithms perform equally. At a confidence level of \(\alpha=0.05\), \(q_{\alpha}=2.724\), resulting in a critical difference (\(CD\)) value of 3.51. The statistical results are shown in Figure 6. As observed in the figure, the proposed algorithm performs significantly better than EDDM_NB, DDM_HT, DDM_NB, and EDDM_HT in terms of delay detection. In Figure 7, each plot corresponds to a different dataset from Table 6. The vertical axis represents the \(FEDP\) metric calculated by Equation (4), with the values on the axis represented as powers of \(2^{n}\). The horizontal axis lists the algorithms from left to right: DNN+AE-DD, DDM_NB, DDM_HT, EDDM_NB, EDDM_HT, HDDM_W_NB, HDDM_W_HT, ADWIN_NB, and ADWIN_HT. In Figure 7, two distinct colors are used to represent the delay, with orange indicating the best result for the current metric (for values exceeding 10,000, 10,000 is used for representation). The observation results reveal that the DNN+AE-DD algorithm performs particularly well on certain datasets, such as reducing the detection delay to a very small range on datasets like HYP. Other algorithms also demonstrate optimal performance on various datasets. Therefore, we can conclude that the DNN+AE-DD is effective in detecting concept drift in the case of a single drift occurrence. In Figure 7, the performance of the DNN+AE-DD in detecting abrupt concept drift is generally inferior to that of other algorithms across most datasets. The possible reason for this could be the short duration of abrupt drift events, making them harder to detect, or the overlap between the distributions of old and new concepts, which complicates detection in the short term. This hypothesis is further supported by the observation of the DNN+AE-DD's performance on other datasets with gradual and incremental drifts. In gradual and incremental drift scenarios, there is a transitional period during which the data distribution changes over time. Specifically, in gradual drift, data points from the new distribution gradually increase, while data from the old distribution decrease. The classification boundaries between the old and new distributions may overlap during \begin{table}
\begin{tabular}{l c 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{3-10}  & & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** & **NB** & **HT** \\ \hline ACR\_a & 2952.11 (4) & 4925.53 (6) & 5000.00 (8) & 5000.00 (8) & 5000.00 (8) & **473.00 (0)** & 783.00 (2) & 4192.77 (5) & 2504.60 (3) \\ SE\_a & **6.12** (7) & 704.18 (3) & 4908.36 (7) & 4904.26 (6) & 1246.66 (2) & 5000.00 (8.5) & 5000.00 (8.5) & 776.28 (4) & 3306.47 (5) \\ Sine\_a & 11.79 (3) & 291.79 (7) & 194.57 (2) & 1211.62 (9) & 977.33 (8) & 8.00 (2) & **7.00 (1)** & 127.64 (5) & 79.00 (4) \\ Mixed\_a & 15.98 (3) & 225.16 (7) & 104.31 (5) & 1066.53 (9) & 404.08 (8) & **5.00 (1)** & 6.00 (2) & 79.00 (4) & 110.68 (6) \\ ACR\_g & **14.25** (3) & 193.26 (4) & 5500.00 (8) & 5500.00 (8) & 5500.00 (8) & 5500.00 (8) & 495.00 (2) & 1287.00 (4) & 4903.68 (6) & 2350.40 (5) \\ SE\_g & **8.96** (1) & 1608.05 (4) & 5500.00 (8) & 1363.93 (9) & 322.45 (2) & 5500.00 (8) & 5500.00 (8) & 2681.41 (6) & 1668.32 (5) \\ Sine\_g & **19.39** (1) & 1083.31 (7) & 712.03 (6) & 1872.98 (9) & 1113.21 (8) & 256.00 (2) & 313.00 (3) & 467.00 (4) & 467.64 (5) \\ Mixed\_g & **10.71** (9) & 925.01 (8) & 518.99 (6) & 1660.59 (9) & 785.70 (7) & 256.00 (2) & 263.00 (3) & 323.32 (5) & 307 (4) \\ HYP\_i & **1.00** (1) & 5500.00 (7) & 5500.00 (7) & 4600.00 (3) & 389.28 (2) & 5500.00 (7) & 5500.00 (7) & 4892.18 (4) & 4937.60 (5) \\ \hline Average rank & **1.78** & 5.94 & 6.83 & 7.11 & 5.89 & 3.78 & 4.22 & 4.78 & 4.67 \\ \hline \hline \end{tabular}
\end{table}