## 4 Experiment Evaluation
### Experimental Settings  
This section describes the relevant settings of the experiments, including the comparison algorithms, experimental environment, and evaluation metrics. In this study, the data stream mining framework MOA [22] is utilized to implement the proposed drift detectors VFDDMs. The performance of VFDDMs is discussed by comparing them with classic or state-of-the-art drift detection algorithms such as FHDDM, MWDDM(MWDDM_H), MDDM, WMDDM, BDDM, RDDM, DDM, HDDM_A, and HDDM_W. For ease of comparison, we conducted the following settings:  
(1) The window size \(n\) is set to 50, and the experiments are conducted under single-window conditions. The window size will affect the detection of different types of drifts. Smaller windows are suitable for detecting abrupt drifts, while larger windows are better for detecting gradual drifts. In literature [7], the authors used two sliding windows of sizes 25 and 100 to detect abrupt and gradual drifts, respectively. In our study, we adopted a compromise in the parameter settings, allowing us to evaluate both types of drifts simultaneously. In all testing methods, the confidence level \(\delta\) was uniformly set to \(10^{-7}\), a commonly used approach in the field of drift detection. The confidence level \(\delta\) is a parameter that adjusts the strictness of the drift detection method. With a given confidence level \(\delta\), the detected concept drift theoretically has a confidence of \(1-\delta\). Therefore, the smaller the \(\delta\), the greater the confidence in the drift alert, and vice versa. Regarding algorithm performance, a smaller \(\delta\) means stricter detection criteria and more precise detection results, and vice versa. (2) Unless otherwise specified in the respective papers of the comparison algorithms, the weighting method is uniformly set to linear weighting. Additionally, the base weighting coefficient is uniformly set to 0.01. This weighting factor has been adopted by several studies, such as in references [7; 16]. The weighting factor affects the detection speed of the drift detector. Generally, a higher weighting factor reduces the detection delay but comes with the drawback of a higher false positive rate. Therefore, the weighting factor should not be set too high. (3) The parameter for the transition of the warning phase in BDDM under the NB classifier is adjusted to 0.5, meaning that drift detection is triggered when \(p_{max}-p\geq 0.5p_{max}\), aiming to achieve a higher level of drift detection performance. (4) For WMDDM, the decay of the impact factor \(\lambda\) of its weight setting after entering the warning phase is set to linear decay. (5) All other parameters of the comparison algorithms, not mentioned explicitly, are kept at their default values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Category** & **Name** & **Instances** & **Attributes** & **Labels** & **Noise** & **Drifts** & **Type** \\ \hline \multirow{4}{*}{Synthetic} & Sine & 100,000 & 2 & 2 & 10\% & 4 & Abrupt \\  & Mixed & 100,000 & 4 & 2 & 10\% & 4 & Abrupt \\  & Circles & 100,000 & 2 & 2 & 10\% & 3 & Gradual \\  & LED & 100,000 & 24 & 10 & 10\% & 3 & Gradual \\ \hline \multirow{4}{*}{Real} & Covertype & 581,012 & 53 & 7 & & \\  & Electricity & 45,312 & 9 & 2 & & \\ \cline{1-1}  & Pokerhand & 829,201 & 10 & 10 & Unknown & \\ \cline{1-1}  & Spam & 10,000 & 500 & 2 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed information about the synthetic and real datasets. This study considers two models, Naive Bayes (NB) and Hoeffding Tree (HT), as the base classifiers for the experiments. Both base classifiers mentioned above use default parameters provided by MOA. Experiments are run on Intel Core i5 (Dell Inspiron 5402 made in Beijing, China) @ 2.4 GHz with 16 GB of RAM running Windows 10. This experiment will introduce the evaluation metrics used: Firstly, the classification accuracy of the base classifier is employed to assess the performance of the drift detection algorithm.