Algorithm 1. K-Anonymity Privacy Protection Algorithm for Multi-Dimensional Data Against Skewness and Similarity Attacks (KAPP)

Input: original multi-dimensional data Output: anonymous multi-dimensional data 1: n = 6000; k = 7; m = 30; Maxit = 200; sas = 6; t = 0.1; 2: Deleting all identifier data, and converting categorical data to numerical value; 3: while (current solution zi ≤ m) do 4:  while (current cluster center j ≤ k) do 5:   $cs{a}_{si}=rs{a}_{si}\times (upsa-dnsa)+dnsa$; 6:   end 7: end 8: while (current iteration it ≤ Maxit) do 9:   while (current solution zi ≤ m) do 10:    $u_j^q=\frac{1}{Dist{(r_j,c_q)}^2}/{\displaystyle \sum _{l=1}^k\frac{1}{Dist{(r_j,c_l)}^2}}$, $f_{zi}={\displaystyle \sum _{q=1}^k{\displaystyle \sum _{j=1}^n{(u_j^q)}^e\times Dist(r_j,c_q)}}$; 11:   end 12:   while (current solution zi ≤ m) do 13:     $HR=ran{d}_{-2}^2\times ({\sin }^{op}(\frac{\pi }{2}\times \frac{it}{Maxit})+\cos (\frac{\pi }{2}\times \frac{it}{Maxit})-1)+ran{d}_{-3}^3\times (1-\frac{it}{Maxit})$; 14:     if (HR ≥ 1) then 15:      if ($P_1$ ≥ $ran{d}_0^1$) then 16:       $x(it+1)=BV(it)-|ran{d}_0^2\times (BV(it)+H(it))\times \frac{1}{2}-x(it)|\times HR$; 17:      else 18:       $x(it+1)=ran{d}_0^1\times ((upsa-dnsa)\times ran{d}_0^1+dnsa)+BV(it)-HR$; 19:      end if 20:     else if (1 ≥ HR ≥ 0.5) then 21:      if ($P_2$ ≥ $ran{d}_0^1$) then 22:      $x(it+1)=(HR+ran{d}_0^1)-BV(it)+x(it)\times |ran{d}_0^2\times BV(it)-x(it)|$; 23:     else 24:       $x(it+1)=BV(it)\times (1-(\frac{ran{d}_0^1\times x(it)}{2\times \pi })\times \cos (x(it))-(\frac{ran{d}_0^1\times x(it)}{2\times \pi })\times \sin (x(it)))$; 25:     end if 26:    else 27:     if ($P_3$ ≥ $ran{d}_0^1$) then 28:        $x(it+1)={\omega }_1\times B{V}_1(it)\times (1-\frac{x(it)\times HR}{B{V}_1(it)-x{(it)}^2})+{\omega }_2\times B{V}_2(it)\times (1-\frac{x(it)\times HR}{B{V}_2(it)-x{(it)}^2})$; 29:     else 30:      $x(it+1)=BV(it)-|BV(it)-x(it)|\times HR\times Levy$; 31:     end if 32:    end if 33:  end 34: end 35: Selecting the most similar data to form n/k equivalence classes; 36: while (current equivalence class v ≤ n/k) do 37:      $SAD{V}_z=\sqrt{{\displaystyle \sum _{h=1}^{a}SAD{N}_z^h}+{\displaystyle \sum _{f=1}^{b}SAD{C}_z^f}}$; 38:     while ($SAD{V}_z>t$) then 39:     Combining the most similar equivalence classes to the quasi-identifier data; 40:   end 41: end 42: Generalizing data and outputting anonymous multi-dimensional data;