Algorithm 2: Pseudo-code of PFA-GMM

Input: The set of data points$\mathit{X}=\{{\mathit{x}}_1,{\mathit{x}}_2,\cdots ,{\mathit{x}}_{\mathit{n}}\}$, Maximum iterations, Population numbers Output: The optimal clustering result 1.  Initialize the population 2.  Select data points randomly and determine the number of clusters C 3.  Generate the initial population and applying through GMM 4.  Calculate the fitness function according to EM 5.  Choose population with the best fitness value as Pathfinder 6.  While K < maximum number of iterations 7.       For i = 1 to maximum number of populations 8.              Update positions of members using Equation (2) 9.              Calculate fitness value of members through EM 10.      End 11.      If best fitness < fitness of Pathfinder 12.             Pathfinder = best member 13.             Fitness = best fitness 14.      End 15.      α and β = random number in [1, 2] 16.      Generate new A and ε 17.      Update the position of Pathfinder using Equation (1) 18.      If new Pathfinder is better than old 19.             Update Pathfinder 20.             Calculate fitness value 21.      End 22. Assign data points to final cluster centroids