# Concept Drift Detection Based on Deep Neural Networks and Autoencoders
## 1 Introduction  
In the era of big data, the exponential growth of information generated from sources such as social media [1, 2], online transactions [3, 4], and credit card fraud [5, 6] results in the continuous production of vast amounts of data, commonly referred to as data streams. Unlike traditional static data, data streams are characterized by their infinite and dynamic nature, which not only presents significant challenges for conventional model training and learning but also introduces a critical issue--concept drift [7]. Assuming that a data stream follows a specific distribution, concept drift refers to a change in this distribution over time, causing the data stream to follow different distributions at different time points. If, at time \(t\), the data follow distribution \(D_{t}(x,y)\) and, at time \(t+1\), the data stream follows distribution \(D_{t+1}(x,y)\), concept drift [8] is said to occur at time \(t+1\), if \(D_{t}(x,y)\
eq D_{t+1}(x,y)\). The occurrence of concept drift typically leads to a significant decline in performance metrics, such as classification accuracy and precision, for the current model in the short term, making the model unsuitable for the post-drift data stream. Therefore, when processing data streams, it is essential to account for the potential issue of concept drift. Currently, approaches for handling concept drift can be categorized into two main types: concept drift detection and concept drift adaptation [9]. The objective of concept drift adaptation is to enhance the model's ability to adjust to changing data. For streaming data, regardless of whether drift occurs, the focus is on the passive adjustment and adaptation of the model to the current data. This involves improving the model's generalization and representation capabilities for the current data. In contrast, concept drift detection takes a proactive approach, aiming primarily to identify whether concept drift has occurred in the data stream. The focus of drift detection is on identifying the time points, duration, and other characteristics of the drift, i.e., determining whether concept drift has occurred at each moment in time. Concept drift detection and adaptation are not mutually exclusive. When the model's drift detection is accurate, it can assist adaptation by further enhancing the model's representation capabilities and robustness. Moreover, timely detection can prevent unnecessary updates to the model, saving time and improving its efficiency in handling concept drift in streaming data. This leads to a more effective and responsive system for managing concept drift. Consequently, the primary focus of this paper is on concept drift detection. Effective concept drift detection methods have significant applications in areas such as fraud detection, disease monitoring, and industrial equipment maintenance. In fraud detection, concept drift detection methods enable fraud detection models to identify and adapt to emerging fraud patterns, thereby mitigating the negative consequences of fraudulent activities. In disease monitoring, patients' physical conditions may change as treatment progresses or the disease advances. Concept drift detection methods aid in capturing these physiological and pathological changes in a timely manner, enabling doctors to detect and intervene early, while also adjusting treatment plans in real time. In the Municipal Solid Waste Incineration (MSWI) process [10], harmful gases such as dioxins may be generated due to factors such as industrial environments or equipment wear. This necessitates the monitoring of parameters like temperature and humidity during the MSWI process. Concept drift detection models can facilitate the real-time and accurate measurement of these parameters, thereby reducing harmful gas emissions.