1 Pertemuan 12 WIDROW HOFF LEARNING Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1
2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Membuktikan Widrow Hoff Learning dengan contoh aplikasi.
3 Outline Materi Jaringan Adaline. LMS Algorithm.
4 ADALINE Network w i w i1 w i2 w iR =
5 Two-Input ADALINE
6 Mean Square Error Training Set: Input:Target: Notation: Mean Square Error:
7 Error Analysis The mean square error for the ADALINE Network is a quadratic function:
8 Stationary Point Hessian Matrix: The correlation matrix R must be at least positive semidefinite. If there are any zero eigenvalues, the performance index will either have a weak minumum or else no stationary point, otherwise there will be a unique global minimum x*. If R is positive definite:
9 Approximate Steepest Descent Approximate mean square error (one sample): Approximate (stochastic) gradient:
10 Approximate Gradient Calculation
11 LMS Algorithm
12 Multiple-Neuron Case Matrix Form:
13 Analysis of Convergence For stability, the eigenvalues of this matrix must fall inside the unit circle.
14 Conditions for Stability Therefore the stability condition simplifies to 12 i –1– Since,. (where i is an eigenvalue of R)
15 Steady State Response If the system is stable, then a steady state condition will be reached. The solution to this equation is This is also the strong minimum of the performance index.
16 Example BananaApple
17 Iteration One Banana
18 Iteration Two Apple
19 Iteration Three