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Widrow -Hoff Learning

Widrow -Hoff Learning. Outline. 1 Introduction 2 ADALINE Network 3 Mean Square Error 4 LMS Algorithm 5 Analysis of Converge 6 Adaptive Filtering. Introduction.

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Widrow -Hoff Learning

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  1. Widrow-Hoff Learning

  2. Outline • 1 Introduction • 2 ADALINE Network • 3 Mean Square Error • 4 LMS Algorithm • 5 Analysis of Converge • 6 Adaptive Filtering

  3. Introduction • In 1960, Bernard Widrow and his doctoral student Marcian Hoff introduced the ADALINE (ADAptiveLInearNEuron)network and LMS(Least Mean Square) algorithm.

  4. Perceptron Network • Figure: a=hardlim(Wp+b)

  5. ADALINE Network • Figure: a=purelin(Wp+b)=Wp+b

  6. Single ADALINE

  7. decision boundary

  8. Mean Square Error

  9. Mean Square Error(conti.)

  10. Mean Square Error(conti.)

  11. Error analysis

  12. Error analysis(conti.) d = -2h and A = 2R definite = 0

  13. Example 1

  14. Example 1(conti.)

  15. Example 1(conti.)

  16. Approximate Steepest Descent

  17. Approximate Gradient

  18. Approximate Gradient(conti.)

  19. Approximate Gradient(conti.)

  20. LMS Algorithm

  21. LMS Algorithm (conti.)

  22. Example 2

  23. Example 2(conti.) , W(0)=

  24. Example 2(conti.)

  25. Example 2(conti.)

  26. Example 2(conti.)

  27. Analysis of Convergence

  28. Analysis of Convergence(conti.)

  29. Analysis of Convergence(conti.)

  30. Example 3

  31. Perceptron rule V.S. LMS algorithm

  32. Perceptron rule V.S. LMS algorithm(conti.)

  33. Perceptron rule V.S. LMS algorithm(conti.)

  34. Perceptron rule V.S. LMS algorithm(conti.)

  35. Adaptive Filtering

  36. Tapped Delay Line

  37. Adaptive Filter

  38. Adaptive Noise Cancellation

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