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A. F. R. Rahman M. C. Fairhurst BCL Computers Inc. University of Kent

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.

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A. F. R. Rahman M. C. Fairhurst BCL Computers Inc. University of Kent

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  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: • Strengthsand 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!

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