1. DecisionCombination of Multiple Classifiers for Pattern Classification: Hybridization of Majority Voting and Divide and Conquer Techniques A. F. R. Rahman M. C. Fairhurst BCL Computers Inc. University of Kent Santa Clara, Calif, USA Canterbury, Kent, UK

2. Presentation Outline Multiple Expert Classification Majority Voting Technique Divide and Conquer Technique Concept of Hybridization Problem Selection (Database/Experts) Performance Discussion and Conclusion

3. Basic Problem Statement Given a number of experts working on the same problem, is group decision superior to individual decisions?

4. Ghosts from the Past… Jean-Charles de Borda (1781) N. C. de Condorcet (1785) Laplace (1795) Issac Todhunter (1865) C. L. Dodgson (Lewis Carrol) (1873) M. W. Crofton (1885) E. J. Nanson (1907) Francis Galton (1907)

5. Is Democracy the answer? Infinite Number of Experts Each Expert Should be Competent

6. How Does It Relate to Pattern Classification? Each Expert has its: Strengths and Weaknesses Peculiarities Fresh Approach to Feature Extraction Fresh Approach to Classification But NOT 100% Correct!

7. Practical Resource Constraints Unfortunately, We Have Limited Number of Experts Number of Training Samples Feature Size Classification Time Memory Size

8. Solution Clever Algorithms to Exploit Experts –Complimentary Information –Redundancy: Check and Balance –Simultaneous Use of Arbitrary Features and Classification Routines

9. Majority Voting At least k classifiers have to agree, when k = n/2 + 1 (n even) k = (n+1)/2 (n odd)

10. Majority Voting: Analysis Probability that x classifiers would arrive at the correct decision: and at wrong decision is: The Precondition of Correctness (Condorcet) is

11. Majority Voting: Analysis (cont.) Assuming x and y to be constant, Since, So when x and y are given, as increases, increases continuously from 0 to infinity.

12. Divide and Conquer Individual Solution Final Solution

13. Divide and Conquer: Analysis

14. Combined Structure: Divide and Conquer with Consensus

15. Selection of a Database Handwritten Characters (NIST) Collected off-line Total samples of over 10,000 characters Size Normalized to 32X32 Numeral Classes 0-9

16. Selected Classifiers Binary Weighted Scheme (BWS) Frequency Weighted Scheme (FWS) Multi-layered Perceptrons (MLP) Moment based Pattern Classifier (MPC) (using Maximum Likelihood Method)

17. Performance of Individual Classifiers

18. Performance of Decision Combination Methods

19. Implementation of Divide and Conquer with Consensus

20. Performance of the Proposed Method

21. Comparison of Throughput

22. Throughput of Combination Methods

23. Conclusion Group Decisions Are often SUPERIOR to Individual Decisions Multiple Expert Solutions can be Made more Robust by incorporating a priori information about the task domain Multiple Expert Solutions Does NOT automatically mean a Slower System!