PART 10 Pattern Recognition 1. Fuzzy clustering 2. Fuzzy pattern recognition 3. Fuzzy image processing FUZZY SETS AND FUZZY LOGIC Theory and Applications.

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Presentation transcript:

PART 10 Pattern Recognition 1. Fuzzy clustering 2. Fuzzy pattern recognition 3. Fuzzy image processing FUZZY SETS AND FUZZY LOGIC Theory and Applications

Fuzzy clustering Fuzzy c-means clustering method 2

Fuzzy clustering 3

4

Fuzzy c-means algorithm 5

Fuzzy clustering 6

7

8

9

Clustering by Equivalence The fuzzy clustering problem can be viewed as the problem of identifying an appropriate fuzzy equivalence relation on given data. It usually cannot be done directly, we can readily determine a fuzzy compatibility relation (reflexive and symmetric) in terms of an appropriate distance function applied to given data. Then, a meaningful fuzzy equivalence relation is defined as the transitive closure of this fuzzy compatibility relation. 10

Fuzzy clustering Distance function 11

Fuzzy clustering Theorem

Fuzzy clustering Example

Fuzzy clustering 14

Fuzzy clustering 15

Fuzzy clustering 16

Fuzzy clustering 17

Fuzzy clustering Example

Fuzzy clustering 19

Fuzzy clustering 20

Fuzzy clustering 21

Fuzzy clustering 22

Fuzzy clustering Membership-Roster method 23

Fuzzy clustering Example

Fuzzy clustering 25

Fuzzy clustering 26

Fuzzy clustering 27

Fuzzy clustering 28

Fuzzy clustering Fuzzy syntactic method 29

Fuzzy clustering Grammar 30

Fuzzy clustering Fuzzy Grammar 31

Fuzzy clustering Example

Fuzzy clustering 33

Fuzzy clustering 34

Fuzzy clustering 35

Fuzzy clustering 36

Fuzzy clustering 37

Fuzzy clustering 38

Fuzzy image processing Fuzzy matrix 39

Fuzzy image processing Example

Fuzzy image processing 41

Fuzzy image processing 42

Fuzzy image processing 43

Fuzzy image processing 44

Fuzzy image processing 45

46 Exercises