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Table 3 CMG algorithm description

From: Air quality forecasting based on cloud model granulation

Algorithm: CMG (TS, winSize, n)

Input: Time series——TS,

 Granulating window width——winSize,

 A number of days to be predicted——n.

Output: Qualitative predicted feature sequence of cloud model \( {\widehat{E}}_{\mathrm{xi}},{\widehat{E}}_{\mathrm{ni}},{\widehat{H}}_{\mathrm{ei}}\left(i=1,2,\dots, n\right). \)

Algorithm steps:

A. Granulating the TS by cloud model, the digital feature sequence E x , E n , H e of TS is generated.

 a-1. Firstly, the original data series is converted into the granular unit data series according to the window width.

 a-2. Second, for each granular unit, the sample mean of each granular unit is calculated \( \overrightarrow{X}=\frac{1}{n}\sum \limits_{i=1}^n{x}_i \),which is the estimated value of expectation E X .

 a-3. Then, it calculates the sample variance \( {S}^2=\frac{1}{n-1}\sum \limits_{i=1}^n{\left({x}_i-\overline{X}\right)}^2 \) and first order sample absolute center moments \( \frac{1}{n}\sum \limits_{i=1}^n\left|{x}_i-\overline{X}\right| \) of each granular;

 a-4. Finally, it calculates the entropy \( {E}_n=\sqrt{\frac{\pi }{2}}\times \frac{1}{n}\sum \limits_{i=1}^n\left|{x}_i-{E}_X\right| \) and hyper entropy \( He=\sqrt{S^2-{E_n}^2} \).

B. Regression prediction of E x by SVR.

 b-1. First of all, it uses the grid search method to find the best kernel parameters for E X .

 b-2. Then, it established the regression prediction model of E X by the above-selected parameter.

 b-3. Finally, it used this model to predict the expectation Ex.

C. Regression prediction of E n by SVR.

 c-1. First, this algorithm uses grid search method to find the best kernel parameters for E n .

 c-2. Then, it established the regression prediction model of E n by the above-selected parameter.

 c-3. Finally, it used this model to predict the entropy E n .

D. Regression prediction of He by SVR.

 d-1. First, it uses the grid search method to find the best kernel parameters for He.

 d-2. Then, it established the regression prediction model of He by above best parameter.

 d-3. Finally, using the model d-2 to predict He.