## 4 Experiment Evaluation  
### Datasets  
To validate the effectiveness of VFDDM, we plan to conduct experiment evaluations on both synthetic and real datasets. This section will provide detailed information about the datasets used in the experiments. The synthetic data streams used in this study are based on the MOA framework [22], allowing for the definition of concept drift positions, frequencies, and durations under various conditions [23]. In the experiments, the synthetic data streams are uniformly set to a scale of 100,000 instances, with 10% noise included. For abrupt concept drift data streams, drift positions are set every 20,000 instances, occurring at positions 20,000, 40,000, 60,000, and 80,000. For gradual concept drift data streams, drifts occur every 25,000 instances, at positions 25,000, 50,000, and 75,000. Each type of data stream generator follows the aforementioned rules for random generation. The four synthetic data stream generators used in our research are as follows:  
**Sine--_Abrupt drift._** This generator sets two attributes, \(x\) and \(y\), distributed uniformly in the interval [0,1]. Classification is performed based on the function \(y=\sin(x)\), where instances below the curve are labeled as positive class, and instances above are labeled as negative class. During concept drift, the decision boundary reverses. **Mixed--_Abrupt drift._** This generator sets two attributes, \(x\) and \(y\), uniformly distributed in the interval [0,1], along with two additional bool variables, \(v\) and \(w\). Instances are labeled as positive class if they satisfy at least two out of the following three conditions: \(v=\text{true}\), \(w=\text{true}\), \(y<0.5+0.3\sin(2\pi x)\). During concept drift, the decision boundary reverses. **Circles--_Gradual drift._** This generator sets two attributes, \(x\) and \(y\), uniformly distributed in the interval [0,1], and incorporates four types of circle equations, representing four concepts. Label categories are determined based on whether the point \((x,y)\) lies inside or outside the circle, assigning positive or negative classes accordingly. Concept drift is induced by altering the circle equations. **LED--_Gradual drift._** The classification model aims to predict digits displayed on a 7-segment display, with each digit having a 10% chance of being displayed. The generator sets 7 relevant attributes along with 17 irrelevant attributes. Concept drift is simulated by swapping relevant attributes. The Sine, Mixed, LED, and Circles synthetic dataset generators we used are widely applicable in the field of concept drift detection and have been extensively used in studies such as [6; 16; 17; 24]. These generators can define the position and length of concept drift, making them suitable for evaluating the performance of drift detectors. Additionally, these simulation data generators are also provided within the MOA [22], ensuring high applicability for the datasets used in our experiments. To evaluate VFDDM's performance across different types of concept drift, we specifically selected two abrupt drift data stream generators (Sine and Mixed) and two gradual drift data stream generators (LED and Circles). This selection ensures the comprehensiveness of our experiments. Meanwhile, we also utilize several classic real-world datasets to validate the performance of VFDDM. The descriptions of these real datasets are provided below:  
**Forest Covertype**[25]--This dataset consists of 54 attributes and 581,012 instances, describing the forest cover types of 30 m \(\times\) 30 m wilderness areas in four regions of the Roosevelt National Forest, obtained from the United States Forest Service Information Systems. **Electricity**[25]--Originating from the New South Wales electricity market in Australia, this dataset comprises 45,312 instances and 8 attributes. The task of the classifier is to predict whether the electricity price will rise or fall. Concept drift mainly arises from the occurrence of sudden events (abrupt) or changes in consumer habits (gradual).