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1 Pertemuan 12 WIDROW HOFF LEARNING Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1
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2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Membuktikan Widrow Hoff Learning dengan contoh aplikasi.
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3 Outline Materi Jaringan Adaline. LMS Algorithm.
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4 ADALINE Network w i w i1 w i2 w iR =
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5 Two-Input ADALINE
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6 Mean Square Error Training Set: Input:Target: Notation: Mean Square Error:
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7 Error Analysis The mean square error for the ADALINE Network is a quadratic function:
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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:
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9 Approximate Steepest Descent Approximate mean square error (one sample): Approximate (stochastic) gradient:
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10 Approximate Gradient Calculation
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11 LMS Algorithm
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12 Multiple-Neuron Case Matrix Form:
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13 Analysis of Convergence For stability, the eigenvalues of this matrix must fall inside the unit circle.
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14 Conditions for Stability Therefore the stability condition simplifies to 12 i –1– Since,. (where i is an eigenvalue of R)
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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.
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16 Example BananaApple
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17 Iteration One Banana
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18 Iteration Two Apple
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19 Iteration Three
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