1. Encode the position for each particle as c hy-
perclusters h
j
, j = 1, ..., c, then initialize partition
matrix U and ﬁrst generation of particles.
2. Start the evolution under the current partition ma-
trix U
t
and ﬁtness function J. The PSO updates
position and velocity for each particle. Evolution
continues until an optimal particle that minimizes
the objective function J under the current partition
matrix U
t
is found. Then we get the c hyperclus-
ters h
t+1
j
, j = 1, ..., c.
3. After we get the c hyperclusters h
t+1
j
, we then cal-
culate the new fuzzy partition matrix for each data
point, the updated fuzzy partition matrix U
t+1
would minimize the objectivefunction J under the
current fuzzy hyperclusters.
4. If the algorithm converges or reaches the max-
imum iteration numbers, the computation stops.
Otherwise, go to Step 2.
The convergence condition is similar to that of the
iterative numerical solution.
4 CONCLUSIONS
We have presented a proposed fuzzy hyper-clustering
algorithm for pattern classiﬁcation in microarray
gene expression data. We formulated the objective
function for the proposed hyper-clustering and dis-
cussed possible solutions using numerical and nature-
inspired optimization methods. The proposed cluster-
ing method can be: 1) suitable for overlapping data
samples as fuzzy membership is utilized; 2) compu-
tationally efﬁcient as the calculation for hyperclus-
ters may use generalized eigenvalue decomposition
which is simpler than that in standard SVMs; 3) po-
tential to handle nonlinear data as a kernelized ver-
sion of the proposed method can take advantage of
the kernel trick for nonlinear data analysis; 4) suit-
able for high dimensions small sample sizes data sets
as the supervised version of the proposed method can
be viewed as a variant of SVMs which currently is
known as the best high-dimension small-sample prob-
lem solver. Furthermore, the proposed approach can
be applied to many other different areas, not only con-
ﬁned to microarray gene expression analysis.
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