1. Local Clustering Algorithm DISCOVIR 9-16-2002

2. Image collection within a client is modeled as a single cluster. Current Situation

3. Proposed Improvement Multiple clusters exist in the image collection

4. Group of similar local cluster A

5. Group of similar local cluster B

6. Group of similar local cluster C

7. Clustering Algorithm 3 clustering algorithms are proposed and tested C – set of cluster center X – dataset Goal of clustering : minimize Error

8. Procedure Randomly pick k x j from {X} and assign them as the set {C} as initial cluster center. Find closest cluster center c and update Error change < threshold iterate a certain step? Input dataset and cluster Randomly pick a point from dataset X N Return cluster center Y

9. Shifting Mean (SM) Suppose x j is picked and c i is the closest cluster center Let p be number of times c i wins, initially p=1 Update c i by

10. Competitive Learning (CL) Update c i by t – the current number of iteration so far T – total number of iteration intend to run We choose  by 0.5, 0.3, 0.1

11. Illustration cici xjxj

12. cici xjxj Winner (move closer)

13. Rival Penalized Competitive Learning (RPCL) Suppose c l is the second closest cluster center to x j Update c i by Update c l by We choose  = 0.05 

14. Illustration cici xjxj Winner (move closer) Rival (move away) unchanged

15. Final Steps For each x j,find the closest c i and mark x j belongs to c i Calculate error function Carryout experiments by varying # of iteration, learning rate

16. Results 0.3Error (400)Error (1000)Error (5000) SM151119822277 CL143517981899 RPCL151019742023 5000Error (0.5)Error (0.3)Error (0.1) SM229022771861 CL162718991609 RPCL224820231607 Fixed Iteration Varying learning rate Fixed Learning rate Varying iteration 0.1Error (400)Error (1000)Error (5000) SM231220081861 CL229818881609 RPCL241419481607 Fixed Learning rate Varying iteration

17. Screen Capture

20. Others Other variation  i – initial learning rate  f – final learning rate Interesting link for competitive learning some competitive learning methods some competitive learning methods