Pertemuan 12 WIDROW HOFF LEARNING

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Pertemuan 12 WIDROW HOFF LEARNING

• Matakuliah H0434/Jaringan Syaraf Tiruan
• Tahun 2005
• Versi 1

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Learning Outcomes

• Pada akhir pertemuan ini, diharapkan mahasiswa
• akan mampu
• Membuktikan Widrow Hoff Learning dengan contoh
  aplikasi.

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Outline Materi

• Jaringan Adaline.
• LMS Algorithm.

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ADALINE Network
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Two-Input ADALINE
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Mean Square Error
Training Set
Input
Target
Notation
Mean Square Error
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Error Analysis
The mean square error for the ADALINE Network is
a quadratic function
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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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Approximate Steepest Descent
Approximate mean square error (one sample)
Approximate (stochastic) gradient
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Approximate Gradient Calculation
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LMS Algorithm
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Multiple-Neuron Case
Matrix Form
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Analysis of Convergence
For stability, the eigenvalues of this matrix
must fall inside the unit circle.
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Conditions for Stability
(where li is an eigenvalue of R)
Therefore the stability condition simplifies to
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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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Example
Banana
Apple
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Iteration One
Banana
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Iteration Two
Apple
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Iteration Three