*2.3. Drift Detection Methods*

Since the selected algorithms are not capable of detecting changes in the data distribution, two well-known active drift detection methods (DDM), Adaptive Window (ADWIN) and Kolmogorov–Smirnov Window (KSWIN) [28] were incorporated into them. These methods were selected because the training uses the latest batch of data with the latest training instances and the size of the window is generally determined by the user.

ADWIN accurately keeps a variable-length window of late values; to such an extent that it holds that there has not been a change in the data distribution. This window is additionally isolated into two sub-windows (W0, W1) used to decide whether a change has occurred. ADWIN contrasts the median of W0 and W1 to affirm that they coincide with a similar distribution. Concept drift is identified assuming the distribution correspondence does not hold anymore. After recognizing a drift, W0 is changed by W1 and a new W1 is introduced. ADWIN utilizes a certainty value *δ* ∈ (0, 1) to decide whether the two sub-windows coincide with a similar dispersion [42].

KSWIN is a drift detection method based on the Kolmogorov–Smirnov (KS) measurable test. KS-test is a measurable test without really any suspicion of basic information appropriation. KSWIN keeps a sliding window Ψ of fixed size *n* (window\_size). The last *r* (stat\_size) tests of Ψ are accepted to address the last idea considered as *R*. From the main *n* − *r* examples of Ψ, *r* tests are consistently drawn, addressing an approximated last concept *W*. The KS-test is performed on the windows *R* also *W*, of a similar size. KS-test looks at the distance of the observational aggregate data distribution *dist*(*R*, *W*) [27].

A sudden change is distinguished by KSWIN if:

$$dist\left(R, \mathcal{W}\right) > \sqrt{-\frac{\ln \alpha}{r}}\tag{1}$$

where *α* is the probability for the test statistic of the KS-test, and *r* is the size of the statistic window.

The reason for using methods based on window size was because the training utilizes the last batch of data with the last training set. The window of fixed size approach is the least complex rule and the window size is usually decided by the user. By having data on the time size of the change, a window of the fixed size approach is a valuable decision [11].
