Fuzzy dm

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  • 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.


  • 1. Fuzzy Clustering By:- Akshay Chaudhari
  • 2. Agenda Introduction Fuzzy C-Mean clustering Algorithm Complexity analysis Pros. and cons. References
  • 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.
  • 4. ApplicationsImage segmentation Medical imaging X-ray Computer Tomography (CT) Magnetic Resonance Imaging (MRI) Position Emission Tomography (PET)Image and speech enhancementEdge detectionVideo shot change detection
  • 5. Fuzzy C-means Clustering
  • 6. Fuzzy C-means Clustering
  • 7. Fuzzy C-means Clustering
  • 8. Fuzzy C-means Clustering
  • 9. Fuzzy C-means Clustering
  • 10. Fuzzy C-means Clustering
  • 11. Fuzzy C-means Clustering
  • 12. Fuzzy C-Mean Algorithm1. Select an initial fuzzy pseudo-partition, i.e. ,assign values to all uij.2. repeat3. 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.
  • 13. Algorithm
  • 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
  • 17. References http://home.dei.polimi.it/matteucc/Clustering/tutorial_h tml/cmeans.html http://en.wikipedia.org/wiki/Fuzzy_clustering Section 9.2 from Introduction to Data Mining by Tan, Kumar, Steinbach
  • 18. Thank You …..