Knowledge modelling by using clustering method Fuzzy C means

1. KNOWLEDGE MODELING BY
USING CLUSTERING
METHOD: FUZZY C-MEANS

2. GENERAL INFORMATION:
• Clustering is one of the most essential processes in pattern recognition, since it
plays a key role in finding the structures in data.
• Fuzzy clustering can be divided into two basic groups, namely fuzzy c-means
clustering (FCM) based on fuzzy partitions, and fuzzy hierarchical clustering
method, based on fuzzy equivalence relations. Other methods derived from the two
above were also proposed by researchers

3. THE AIM OF FUZZY C-MEANS CLUSTERING:
• The aim of this work is to apply fuzzy c-means clustering model to image
segmentation process.
• Texture segmentation problem is one of the fundamental one in the pattern
recognition and image processing, such as in remote sensing, medical imaging,
textile products inspection etc. Given an image with multiple texture regions,
fuzzy c-means algorithm can be used to cluster the image vectors into several
classes, each corresponding to the different regions. The output is the segmented
image which can be further processed for noise removal if required.

4. GENERAL INFORMATION ABOUT FUZZY C-
MEANS CLUSTERING:
• The Fuzzy c-means is one of the most popular ongoing area of research among all
types of researchers including Computer science, Mathematics and other areas of
engineering, as well as all areas of optimization practices. Several problems from
various areas have been effectively solved by using FCM and its different variants.
• Fuzzy c-means clustering model was first introduced by Dunn in 1974 and later in
1973 extended and generalized by Bezdek

5. FCM
The algorithm for fuzzy c-means clustering consists of an iterative clustering method
whose output is optimal ‘c’ partition, obtained by minimizing the objective function
FCM.The basic FCM algorithm is formulated as follows:
• Step-1: Randomly initialize the
membership matrix using this equation,
• Step-2: Calculate the Centroid using
equation,
• Step-3: Calculate dissimilarly between
the data points and Centroid using the
Euclidean distance
• Step-4: Update the New membership
matrix using the equation,
Here m is a fuzzification parameter.
The range m is always [1.25, 2]
• Step-5: Go back to Step-2, unless the
centroids are not changing.

6. EXAMPLE:
• Input: Number of objects=6 Number of clusters=2
X Y C1 C2
1 6 0.8 0.2
2 5 0.9 0.1
3 8 0.7 0.3
4 4 0.3 0.7
5 7 0.5 0.5
6 9 0.2 0.8

7. • Step-1: Initialize the membership matrix.
• Step-2: Find the constraint using the equation

9. Step-3: Find distance
• Centroid 1:
(1,6)(2.4,6.1)=
(2,5)(2.4,6.1)=
(3,8)(2.4,6.1)=
(4,4)(2.4,6.1)=
(5,7)(2.4,6.1)=
(6,9)(2.4,6.1)=
• Centroid 2:
(1,6)(4.8,6.8)=
(2,5)(4.8,6.8)=
(3,8)(4.8,6.8)=
(4,4)(4.8,6.8)=
(5,7)(4.8,6.8)=
(6,9)(4.8,6.8)=

10. Cluster 1 Cluster 2
Datapoint Distance Datapoint Distance
(1,6) 1.40 (1,6) 3.88
(2,5) 1.17 (2,5) 3.32
(3,8) 1.99 (3,8) 2.16
(4,4) 2.64 (4,4) 2.91
(5,7) 2.75 (5,7) 0.28
(6,9) 4.62 (6,9) 2.50

11. • Step-4: Update the membership value
Here m=2, i-first data point, j-first cluster

12. CLUSTER 1

13. CLUSTER 2

14. NEW MEMBERSHIP MODEL IS
X Y C1 C2
1 6 0.7 0.3
2 5 0.6 0.4
3 8 0.5 0.5
4 4 0.5 0.5
5 7 0.1 0.9
6 9 0.3 0.7
• Step-5: Now continue this process until get the same centroids.

15. THANKS FOR ATTENTION!