Table 3. Algorithm 3.

Grouping perturbation algorithm
Input: The data set Sti that needs to be sampled at the time ti, the Predicted value of the sampling node ${\hat{x}}_i^j$
Output: The noise value of sampling point in Sti
for each site j ∈ Stido
Predict statistics ${\hat{x}}_i^j$ using the ARIMA model
If${\hat{x}}_i^j>\tau$then
Let the site j itself as a group, add the group to Gti
Else
add the site j into Φ
Initialize cluster centers ci
whileJ not convergent do
Initialize Membership matrix $U_{ij}=\frac{1}{{\sum }_{k=1}^c{\left(\frac{∥x_j-c_i∥}{∥x_j-c_k∥}\right)}^{\left(\frac{2}{m-1}\right)}}$
Calculated value function $\mathrm{J}={\sum }_i^c{\sum }_{j=1}^n{U}_{ij}^m{∥x_j-c_i∥}^2$
Revised cluster centers
Cluster result: $\mathrm{P}=\left\{{\mathrm{C}}_{\mathrm{j}}:j\text{is a cluster center}\right\}$
Group the site in Φ according to P and add each group to Gki
Introduce Laplace noise into each group Gti
Allocate the group perturbed statistic to each site according to ${\hat{x}}_i^j$
$A\left(g\right)={\sum }_{j=1}^k\sum g\left[j\right]+Lap\left(\frac{\Delta \left(f\right)}{min\left({ϵ}_{g\left[j\right]}\right)}\right)$
return The noise value $A\left(g\left[j\right]\right)=A\left(g\right)∕k$ of sampling point in Sti