Algorithm 1: Pseudocode for construction of adaptive grid space.

Input: dataset $D^d$ and resolution R and coordinate sequence $S{C}_i^D$.

Output: Multidimensional grid space $G^D$.

1: Begin

2: $G^D\leftarrow \varphi$

3: $N\leftarrow$ samples number of $D^d$

4: $d\leftarrow$ dimension of $D^d$

5: for $k$ = 1 to $N$ do

6:    $cellnum\leftarrow 0$

7:    for $i$ = 1 to $d$ do

8:      for j = 1 to R do

9:        if ${sc}_i^D(j-1)\le x_k^d\left(i\right)<{sc}_i^D\left(j\right)$ then

10:          $cellnum\leftarrow cellnum+(j-1)R^{j-1}$

11:          $c\left(i\right)\leftarrow j$

12:    $location\left(C_{cellnum}^D\right)\leftarrow 〈c\left(1\right),c\left(2\right),\cdots ,c\left(d\right)〉$

13:    $mumber\left(C_{cellnum}^D\right)\leftarrow mumber\left(C_{cellnum}^D\right){\cup X}_k^d$

14:    $density\left(C_{cellnum}^D\right)\leftarrow density\left(C_{cellnum}^D\right)+1$

15: if $C_{cellnum}^D\notin G^D$ then

16: $G^D\leftarrow G^D\cup C_{cellnum}^D$