Hybrid Fuzzy Clustering Method Based on FCM and Enhanced Logarithmical PSO (ELPSO)

Algorithm 2

FCM-ELPSO.

	Notations:
	P: the population of ELPSO; ω_initial: the initial inertia weight of ELPSO; : the inertia weight of the particle l; and : acceleration coefficients; : the position of the particle l; : velocity vector of the particle l; : the best position that particle l has achieved at instant t; : the best position achieved by the swarm at instant t; : the membership degree matrix of the particle l; : the fitness value of the particle l; T_PSO: the maximum number of iterations in PSO part; T_FCM: the maximum number of iterations in FCM part; m: the level of cluster fuzziness;
	Input: dataset S and number of clusters C;
	Output: the best position .
	Process:
(1)	Create a swarm with P particles;
(2)	Initialize parameters for ELPSO including size of population P; ω_initial for each particle (l = 1, 2, 3, …, P); and , m;
(3)	Initialize , , and for each particle (l = 1, 2, 3, …, P) and for the swarm;
(4)	do {
	ELPSO:
	Repeat {
(5)	Calculate the membership degree matrix of each particle;
(6)	Calculate the criterion of each particle;
(7)	Calculate the of each particle;
(8)	Calculate the of the swarm;
(9)	Update the velocity of each particle using equation (13);
(10)	Update the position of each particle using equation (14);
(11)	For each particle (l = 1, 2, 3, …, P) update using equation (12);
(12)	store as ;
(13)	t = t + 1;
	}
	Until ELPSO termination condition is met (∗).
	FCM:
	Repeat {
(14)	Calculate membership degrees using equation (7);
(15)	Calculate cluster prototypes using equation (6);
(16)	Calculate the of each particle;
(17)	Calculate the of the swarm;
(18)	store as ;
	}
	Until ELPSO termination condition is met (∗∗)
	While termination condition is not met (∗∗∗)
	return matrix.
	(∗) when it reaches 95 iterations (T_PSO) or there is a variation less than or equal to 0.00001 on criterion J.
	(∗∗) when it reaches 5 iterations (T_FCM) or there is a variation less than or equal to 0.00001 on criterion J.
	(∗∗∗) when it reaches 500 total iterations (ELPSO + FCM) or when there are no changes to the in two consecutive runs of the FCM–PSO (FPSO followed by FCM).