# Benchmarking Change Detector Algorithms from Different Concept Drift Perspectives
## 1 Introduction  
Concept drift refers to the phenomenon where the patterns of a dataset change with time, making it difficult to develop accurate models and predictions [1]. This is a real-life challenge that is particularly acute when dealing with data streams, where the underlying data distribution can evolve rapidly and unpredictably [2]. The problem of concept drift can arise in many different contexts, such as financial forecasting, cybersecurity [3], process mining [4, 5], and environmental sensing [6, 7]. In these domains, it is essential to develop algorithms and techniques that can adapt to changing data distributions and maintain high accuracy over time. One promising approach to addressing concept drift is to use online learning methods, which update models in real time as new data become available [8]. Successful strategies for handling concept drift require a deep understanding of the underlying data-generating processes and the ability to develop flexible and adaptive algorithms, which can learn and evolve over time. Change detectors play a crucial role in addressing concept drift, as these allow for the detection of changes in the statistical properties of data streams [9]. These detectors can be used to identify when a model trained on historical data is no longer accurate due to changes in the underlying data distribution. While the current literature on change detectors provides several established methods, selecting and tuning these techniques for specific types of concept drift can be an additional challenge. The most popular change detectors, or simply detectors, are Adaptive Windowing (ADWIN) [10], PH Page Hinkley (PH) [11], drift detection method (DDM) [12], early drift detection method (EDDM) [13], drift detection methods based on Hoeffding's bounds with the moving average-test (HDDMA), and drift detection methods based on Hoeffding's bounds with the moving weighted average-test (HDDMW) [14]. ADWIN and PH are both based on monitoring the statistics of a sliding window, but they use different statistical approaches. ADWIN calculates the average of the statistics in two different time intervals and compares them to detect a change. Conversely, PH uses the cumulative sum of the differences between the current and previous statistics to detect changes. Both ADWIN and PH are known to be effective in detecting gradual drifts but may struggle with abrupt and incremental drifts. EDDM, DDM, HDDMW, and HDDMA rely on the same principle of monitoring the statistics of a sliding window and detecting changes when the statistics deviate from a baseline. However, they differ in the specific statistics they use, the thresholds they apply, and the way they adapt to different types of concept drift, covering a broad range of drifts. Detecting concept drift is an important task in machine learning applications, with a variety of change detectors available in the literature. However, selecting the most appropriate detector for a given type of concept drift can be challenging. Different detectors may perform better under specific conditions, such as different types, durations, and magnitudes of concept drift. Therefore, carefully evaluating the performances of change detectors in various contexts is critical to ensure their effectiveness in real-world applications. The most popular change detectors in the literature each have their own strengths and limitations for detecting different types of concept drifts. There are many types of concept drift in the literature, which are categorized according to their severity and speed [15]. The most relevant categories are abrupt, gradual and incremental. Abrupt changes are characterized by a sudden and significant change in the data distribution, which can be represented in real-life examples such as an online fraud detection system or a sudden shift in sensor data distribution [16; 17; 18].