3. Introduction
Fuzzy clustering is a method of clustering which
allows one piece of data to belong to two or
more clusters.
In other words, each data is a member of every
cluster but with a certain degree known as
membership value.
This method (developed by Dunn in 1973 and
improved by Bezdek in 1981) is frequently used
in pattern recognition.
12. Fuzzy C-Mean Algorithm
1. Select an initial fuzzy pseudo-partition, i.e. ,assign values
to all uij.
2. repeat
3. Compute the centroid of each cluster using fuzzy
pseudo-partition.
4. Recompute fuzzy pseudo-partition, i.e., the uij.
5. until the centroids don’t change.
14. An example
X=[3 7 10 17 18 20] and assume C=2
0.1 0.2 0.6 0.3 0.1 0.5
Initially, set U randomly U=
0.9 0.8 0.4 0.7 0.9 0.5
N
∑u m
x
ij i
cj = i =1
N
∑u
i =1
m
ij
Compute centroids, cj using , assume m=2
1
uij = 2
C
|| xi − c j || m −1
c1=13.16; c2=11.81
∑ || x − c ||
k =1
i k
Compute new membership values, uij using
0.43 0.38 0.24 0.65 0.62 0.59
U=
New U: 0.57 0.62 0.76 0.35 0.38 0.41
Repeat centroid and membership computation until changes in
membership values are smaller than say 0.01
15. Complexity analysis
Time complexity of the fuzzy c mean algorithm is
O(ndc2i)
Where
i number FCM over entire dataset.
n number of data points.
c number of clusters
d number of dimensions
where… i grows very slowly with n,c and d.
16. Pros. & Cons.
Pros:
Allows a data point to be in multiple clusters
A more natural representation of the behavior of genes
genes usually are involved in multiple functions
Cons:
Need to define c, the number of clusters
Need to determine membership cutoff value
Clusters are sensitive to initial assignment of centroids
Fuzzy c-means is not a deterministic algorithm
Tomograph: Medical instrument which receives X-rays via a special method. Magnetic Resonance Imager (MRI): Diagnostic technique which uses a magnetic field and radio waves to provide computerized images of internal body tissues. Positron Emission Tomography (PET): Technique for creating detailed images of bodily tissues by injecting positron-laden material into the body and recording the gamma rays emitted over a period of approximately two hours.
