using larger windows. Concept drift is perceived by detecting the change in classification precision. However, false concept drift, which is caused by noise, can cause unnecessary updating of the base classifiers and can waste resources. In References [7; 8; 9], the concept drift detection method based on double thresholds can effectively decrease the influence of noise. In Reference [8], the method of comparing the data classification error rate of adjacent windows can detect sudden concept drift. In Reference [9], the method of comparing the minimum values of the classification error rate for each window further improves the detection efficiency of gradual concept drift.  
In addition, using attribute reduction or other dimension reduction methods to improve execution speed has become a key topic in the research of data stream processing. In Reference [2], the number of base classifiers is set to maximum and increased or decreased under different conditions, which saves memory demand. In Reference [10], the classification error rate of each attribute is compared to select important attributes. In Reference [11], the attribute reduction algorithm based on rough sets reduces the computation complexity sufficiently by relaxing the measurement criteria of attribute importance and ensures the distinctiveness of the reduced data using a specific strategy. However, this algorithm uses an attribute importance measure based on the positive region, which is defined as the union of lower approximations. Compared with an attribute reduction algorithm based on information entropy, it deals with system uncertainty poorly [12]. Meanwhile, the difference between base classifiers is the key factor that affects the overall performance of an ensemble system [11] and perturbing the sample attribute space by attribute reduction has become the main approach to increase this difference [13; 14].  
In this paper, we propose an ensemble classification algorithm of data streams based on attribute reduction and a sliding window. In the algorithm, we use double thresholds to detect concept drift and update the sliding window size. We use the data attributes after reduction and nonlinear weights of base classifiers to improve the data classification precision of noisy data streams. Our work in this paper consists of three main parts. Using mutual information, we propose a rough set-based approximate attribute reduction algorithm to decrease the computation complexity of the ensemble classification algorithm and increase the difference between base classifiers. By introducing the sliding window idea of congestion control in the transport layer of a computer network, we propose a size control strategy of sliding windows. A double-threshold concept drift detection method is proposed based on the size control strategy. Based on attribute reduction and the sliding window, we propose an ensemble classification algorithm of noisy data streams to improve the classification precision with low complexity.  
The remainder of this paper is organized as follows. Section 2 describes the problem that we aim to solve by our proposed algorithm in the paper. Section 3 describes the rough set-based approximate attribute reduction algorithm. Section 4 describes the detection method of concept drift. Section 5 describes the ensemble classification algorithm of data streams in detail. Section 6 verifies and analyzes the algorithm performance and Section 7 presents a summary of the study.