IEEE Computational Intelligence Magazine - November 2021 - 15

modularity gain associated with changing
the fuzzy membership values of
network vertices. The simplicity of the
proposed scheme enables efficient modifications,
reducing computational complexity
to a linear function of the
network size, and the number of communities.
Moreover, to further reduce
the complexity of FFMM for very
large networks, multicycle FFMM
(McFFMM) is proposed. The proposed
McFFMM reduces complexity by
breaking networks into multiple subnetworks
and applying FFMM to
detect their communities. Performance
of the proposed techniques is demonstrated
with real- world data and the
Lancichinetti-Fortunato-Radicchi
benchmark networks. Moreover, the
performance of the proposed techniques
is evaluated versus some stateof-the-art
soft overlapping community
detection approaches. Results show that
the McFFMM produces a remarkable
performance in terms of overlapping
modularity with fuzzy memberships,
computational time, number of detected
overlapping nodes, and overlapping
normalized mutual information. "
Fuzzy Density Peaks Clustering, by Z.
Bian, F-L. Chung, and S. Wang,
IEEE Transactions on Fuzzy Systems,
Vol. 29, No. 7, July 2021, pp.
1725-1738.
Digital Object Identifier: 10.1109/
TFUZZ.2020.2985004
" As an exemplar-based clustering
method, the well-known density peaks
clustering (DPC) heavily depends on the
computation of kernel-based density
peaks, which incurs two issues: first,
whether kernel-based density can
facilitate a large variety of data well,
including cases where ambiguity and
uncertainty of the assignment of the
data points to their clusters may exist,
and second, whether the concept of
density peaks can be interpreted and
manipulated from the perspective of soft
partitions (e.g., fuzzy partitions) to
achieve enhanced clustering performance.
In this article, in order to provide
flexible adaptability for tackling
ambiguity and uncertainty in clustering,
a new concept of fuzzy peaks is proposed
to express the density of a data
point as the fuzzy- operator-based coupling
of the fuzzy distances between a
data point and its neighbors. As a fuzzy
variant of DPC, a novel fuzzy density
peaks clustering (FDPC) method FDPC
based on fuzzy operators (especially
S-norm operators) is accordingly devised
along with the same algorithmic framework
of DPC. With an appropriate
choice of a fuzzy operator with its
associated tunable parameter for a clustering
task, FDPC can indeed inherit
the advantage of fuzzy partitions and
simultaneously provide flexibility in
enhancing clustering performance. The
experimental results on both synthetic
and real data sets demonstrate that the
proposed method outperforms or at
least remains comparable to the comparative
methods in clustering perfor
mance by choosing appropriate
pa rameters in most cases. "
IEEE Transactions on
Evolutionary Computation
SAFE: Scale-Adaptive Fitness Evaluation
Method for Expensive Optimization
Problems, by S.-H. Wu, Z.-H. Zhan,
and J. Zhang, IEEE Transactions on
Evolutionary Computation, Vol. 25, No.
3, June 2021, pp. 478-491.
Digital Object Identifier: 10.1109/
TEVC.2021.3051608
" The key challenge of expensive
optimization problems (EOP) is that
evaluating the true fitness value of the
solution is computationally expensive. A
common method to deal with this issue
is to seek for a less expensive surrogate
model to replace the original expensive
objective function. However, this method
also brings in model approximation
error. To efficiently solve the EOP, a
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