# Concept Drift Detection Based on Deep Neural Networks and Autoencoders
## 4 Experiment  
### Datasets  
In this experiment, both synthetic and real-world datasets are used to validate the effectiveness of the proposed method. The synthetic data are generated using the Massive Online Analysis (MOA) toolbox [36] to create drift data and static data (without drift). MOA ([[https://moa.cms.waikato.ac.nz/](https://moa.cms.waikato.ac.nz/)]([https://moa.cms.waikato.ac.nz/](https://moa.cms.waikato.ac.nz/)) (accessed on 10 May 2024)) is a software environment for evaluating algorithms and conducting online streaming data learning experiments, containing numerous stream data generators. This study selects several generators to produce single-drift and multi-drift type data, including Agrawal (AGR), SEA, Sine, Mixed, and Hyperplane (HYP). Details of the synthetic datasets can be found in Tables 1 and 2. In Table 1, the SEA, Sine, Mixed, and AGR datasets were generated with both abrupt and gradual drift types. According to the MOA reference manual, the HYP generator is specifically used to generate incremental data, and its method of generating drift data differs from that of the other datasets. As the classification function of the data cannot be altered, multi-drift data were not generated for the HYP dataset. All datasets contain 10,000 instances and are balanced binary-class datasets. Taking the SEA dataset as an example, when the drift position is set to 5000 and the width to 1, an abrupt SEA is generated. In this case, data before point 5000 correspond to the old concept, while data after point 5000 correspond to the new concept. When the drift position is set to 4500 and the width to 1000, a gradual SEA is generated. In this scenario, data before point \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Datasets** & **Number of Features** & **Number of Samples** & **Drift Position** & **Drift Width** \\ \hline SEA\_a 1 & 3 & 10,000 & 5000 & 1 \\ SEA\_g 2 & 3 & 10,000 & 4500 & 1000 \\ Sine\_a & 2 & 10,000 & 5000 & 1 \\ Sine\_g & 2 & 10,000 & 4500 & 1000 \\ Mixed\_a & 4 & 10,000 & 5000 & 1 \\ Mixed\_g & 4 & 10,000 & 4500 & 1000 \\ AGR\_a & 6 & 10,000 & 5000 & 1 \\ AGR\_g & 6 & 10,000 & 4500 & 1000 \\ HYP\_i 3 & 10 & 10,000 & 4500 & 1000 \\ \hline \hline \end{tabular}  
* The word ‘a’ mentioned means the type of drift is abrupt. 2 The word ‘g’ mentioned means the type of drift is gradual. 3 The word ‘i’ mentioned means the type of drift is incremental.  
\end{table} 
Table 1: Synthetic Data with single drift. Figure 5: Concept drift detection. 4500 correspond to the old concept, and drift begins at point 4500, lasting for 1000 instances. After point 5500, the drift ends, and the remaining data correspond to the new concept. The datasets used in Table 2 are the same as those in Table 1, with the distinction that each dataset contains multiple drifts points and multiple instances of abrupt or gradual drift within the same data volume. In MOA, the SEA and Sine datasets each contain four classification functions (i.e., four different concepts), so we evenly divided the ten thousand data instances among the four concepts, which included three drift points. The AGR dataset contains ten classification functions, resulting in nine drift points, and the drift width for gradual AGR is smaller than for other gradual datasets. The mixed dataset contains only two classification functions, and we utilized it to generate multiple abrupt drifts datasets. So, to maintain consistency with the data volume of the other datasets, we divided the ten thousand data instances into five parts, with four points. For datasets such as SEA that contain multiple abrupt drifts, the concepts follow a step-like progression, meaning each newly appearing concept differs from all the preceding ones, forming entirely new concepts. However, due to the mixed dataset only containing two concepts, the generated data cannot include multiple concepts. As a result, in the case of multiple abrupt drifts, the data from the mixed dataset alternate between the old and new concepts.