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each sample belongs to each category. It can identify
each sample belongs to a category in accordance with the
principle of maximum membership according to the
matrix. We can see from the algorithm that it is better to
cluster for the data of normal distribution, and is more
sensitive to the isolated point.
C. Problems about the Application of FCM
In recent years, cluster analysis has become an
important technique of data mining. Although many
clustering methods obtain a wide range of applications,
there are problems of limitations and adaptability for
every method. To the fuzzy clustering algorithm, FCM
algorithm is the most widely used, but it also has many
issues to exist, such as the number of the cluster must be
preset by users, and select the appropriate number of
clusters is the precondition for a precise clustering, but it
is difficult to determine the number of clustering; as
FCM algorithm is essential a local optimization
technology, which uses the Hill Climbing to find out the
optimal solution for iterating, it is particularly sensitive
to initialize, and easily to fall into the local minimum so
that can’t obtain the global optimal solution.
IV. OPTIMIZATION OF FUZZY CLUSTERING ALGORITHM
The method of intrusion detection based on fuzzy
clustering, FCM often combine with other methods to
detect the intrusion, of course, there are many hybrid
methods, such as the combination of FCM and adaptive
immune system, the application of the average
information entropy, the combination of FCM and
support vector machine, the fuzzy genetic algorithm and
etc.. The paper respectively introduced the research in
recent years on how to obtain the number of clusters and
the optimal solution in the following.
A. Determination of The Number of Clusters
Many studies aimed at the number of FCM clustering
algorithm and the selection of the initial cluster centers,
but the relevant research, only consider the determination
of the number of clusters, or only to select the initial
cluster centers. Ref. [4] introduced a method based on
the average information entropy for the problem of the
determination of the cluster number in FCM algorithm,
and used the density function to obtain the initial cluster
center.
When the division of the cluster is more reasonable,
the data on the attribution of a cluster is more established,
and the information entropy is smaller. Ref. [4] improved
the clustering algorithm based on the information
entropy, it used the average information entropy as the
standard for determining the number of cluster. The
concept of the average information entropy is defined as
follows:
C N
( k ) = −∑∑{ [ uij
× log 2( uij
) + ( − uij
)×
H 1
i= 1 j=
1
( )] N}
log 21−u ij
⑸
First, to define the range of the number of cluster,
C . In (5), uij
indicated the extent of the
u ij
∈ 0,1 , ∀i,
. When
[ ]
min ,C max
sample j belongs to clusteri , [ ] j
k increase from C min
to C
max
, it can create
Cmax − Cmin
+ 1 of H K
( x)
. According to the
regulation, the smaller information entropy value is, the
more established the data belongs to a cluster, and then
select the smallest H K
( x)
, which corresponds to the
cluster number k as the final cluster numberC .
Ref. [5] proposed a fuzzy C-means and support vector
machine algorithm (F-CMSVM) for automatic clustering
number determination; it can solve the issue in fuzzy
C-means algorithm (FCM) that clustering number has to
be pre-defined. It used the algorithm of support vector
machine with a fuzzy membership function and used the
affiliating matrix which obtained by the introduction of
support vector machine into fuzzy C-means algorithm as
the fuzzy membership function, so that each different
input data sample can have different penalty value, then
it can obtain the optimized separating hyper-plane.
For the fuzzy C-means and support vector machine
algorithm, first of all, it suppose that the given data set
can be divided into 2 categories ( k = 2)
, and use the
fuzzy C-means to cluster, then use the affiliating matrix
which obtained by using the algorithm as the fuzzy
membership of the fuzzy support vector machine
algorithm, and train the data sets so that it can access to
the support vector machine and the separating
hyper-plane. To test the assumption, it had proposed a
new standard in the paper: use the d
SV
as the distance
between the two categories. And d
S1
, d
S 2
mean the
average distance between the respective support vector
of S1, S2 and the nearest neighbor points. If
d
SV
≤ min( d
S1,
d
S 2
) , the original dataset can not be
classified, and the assumption is not true; otherwise, it
establish and the original dataset can be divided into two
categories at least.
B. Obtain The Global Optimal Solution
For the problem that it is easy to fall into local
minimum value caused by the sensitive initialization to
FCM, people have been proposed the clustering method
based on genetic algorithm, the method can converge to
the global optimal value at a higher probability, but its’
convergence rate is slower and it will appear the
phenomenon of precocity. To solve the problem, Ref. [6]
used the clonal selection algorithm (CSA) to optimize
the objective function of the unsupervised FCM
clustering algorithm; the clonal selection algorithm used
the mechanism of antibody clone to construct a clone
operator which combines characters of the evolutionary
search, the global search, the stochastic search and the
local search. As CSA based on the clone operator is a
Groupization strategy, it has parallelism and randomness,
so that it can obtain the global optimal solution with a
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