IEEE Computational Intelligence Magazine - November 2020 - 65

non-membership degrees of data points to clusters (Line 13) to
apply the derivative of J(U, V ) [24].
B. A Metaheuristic for Optimizing Clusters

The performance of FCM clustering heavily depends on the
quality of initial cluster centroids [28], [29]. Instead of randomly setting initial cluster centroids, we use a m
- etaheuristic
algorithm, ecogeography-based optimization (EBO) [30], to
optimize initial cluster centroids [29]. The algorithm starts by
initializing a population of solutions, each representing a set
V (0) of c initial cluster centroids. Let J (x) denote the resulting
J(U, V ) value obtained by the FCM method from the initial
cluster centroids of x; each solution x is assigned with an emigration rate E r (x) that is inversely proportional to J (x) and an
immigration rate I r (x) that is proportional to J (x):
J max - J (x) + e
(6)
J max - J min + e
J (x) - J min + e
I r (x) =
(7)
J max - J min + e

E r (x) =

	
	

where J max and J min are the maximum and minimum J( ∙ ) values among the population, respectively, and e is a small positive
number to avoid division-by-zero. In this way, a better solution
has a higher probability of emigrating features to other solutions, while a worse solution has a higher probability of immigrating features from other solutions [31].
The EBO algorithm then continually evolves the solutions
using two migration operators: local migration and global
migration. Local migration updates a solution x at each dimension d by migrating the corresponding dimension of a neighboring solution x @ as follows:
xld = x d + rand (0, 1) · (x @d - x d)(8)

	

where rand (0, 1) produces a random number uniformly distributed in (0, 1), and x @ is selected from all neighbors of x
with a probability proportional to E r (x @).
Global migration updates a solution x at each dimension d
by migrating the corresponding dimensions of both a neighboring solution x @ and a non-neighboring solution x ‡ as follows:
	

xld = )

‡

x @d + rand (0, 1) · (x d - x d), f (x ‡) # f (x @)
(9)
‡
x d + rand (0, 1) · (x d@ - x d), f (x ‡) 2 f (x @)

where x @ is selected from all neighbors of x and x ‡ is selected
from all non-neighboring solutions of x; the selection probabilities are proportional to Er .
EBO uses a parameter h as the probability of performing
global migration and, therefore, (1-h ) as the probability of performing local migration. The value of h dynamically increases
from a lower limit h min to an upper limit h max with generation
g of the algorithm:
	

h = h min

+

g
(h - h min)(10)
g max max

In this study, we use a local random neighborhood structure
[32], which randomly assigns kN neighboring solutions to each
solution in the population (where kN is a parameter set to 3); if
the current best solution has not been updated after a number
tg of consecutive generations, the neighborhood structure is
randomly reset. Algorithm 2 presents the pseudocode of the
EBO algorithm, where Line 4 invokes Algorithm 1 to evaluate
the fitness of each solution (initial centroid setting).
III. Interactive Optimization of Prevention Programs

After clustering the community residents into c groups, we
invite TCM experts to assess the health characteristics of each
cluster (and examine typical residents if possible), and develop
diversified prevention programs according to the characteristics.
Note that the number p of prevention programs approximates,
but does not necessarily equal, the number c of clusters. That is,
the TCM experts typically develop a prevention program
(including a TCM prescription and other supplementary
means such as acupuncture and moxibustion) for a cluster; they

Algorithm 2 The EBO algorithm for enhancing the fuzzy clustering
method.

 1 Randomly initialize a population of solutions (initial set of
cluster centroids);
 2 while the stopping criterion is not satisfied do
 3    foreach solution x in the population do
 4     Use Algorithm 1 to produce the clustering results
(U, V) from the initial cluster centroids of x;
 5    Let x ) be the best solution in the population;
 6    foreach solution x in the population do
 
7     
Compute E r (x) and I r (x) according to Eqs. (6) and
(7);
 8    foreach solution x in the population do
 
9     for d = 1 to n do
10       if rand (0, 1) 1 I r (x) then
11         
Select a neighboring x @ with probability
proportional to E r (x @);
12         if rand (0, 1) 1 h then
13           
Select a non-neighboring x ‡ with probability proportional to E r (x ‡ );
14           
Do global migration according to Eq. (9);
15         else
16           Do local migration according to Eq. (8);
17     if the migrated solution xl is better than x then
18       x ! xl ;
19   Update h according to Eq. (10);
g consecutive generations
20    i f x ) has not been updated for W
then
21      Randomly reset the neighborhood structure;
22  return the clustering result of the best known solution x ).

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