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1 Pertemuan 13 BACK PROPAGATION Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1
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2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menjelaskan konsep Back Propagation.
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3 Outline Materi Algoritma Back Propagation
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4 Multilayer Perceptron R – S 1 – S 2 – S 3 Network
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5 Example
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6 Elementary Decision Boundaries First Subnetwork First Boundary: Second Boundary:
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7 Elementary Decision Boundaries Third Boundary: Fourth Boundary: Second Subnetwork
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8 Total Network
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9 Function Approximation Example Nominal Parameter Values
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10 Nominal Response
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11 Parameter Variations
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12 Multilayer Network
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13 Performance Index Training Set Mean Square Error Vector Case Approximate Mean Square Error (Single Sample) Approximate Steepest Descent
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14 Chain Rule Example Application to Gradient Calculation
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15 Gradient Calculation Sensitivity Gradient
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16 Steepest Descent s m F ˆ n m ---------- F ˆ n 1 m --------- F ˆ n 2 m --------- F ˆ n S m m ----------- = Next Step: Compute the Sensitivities (Backpropagation)
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17 Jacobian Matrix F Ý m n m f Ý m n 1 m 0 0 0f Ý m n 2 m 0 00 f Ý m n S m m =
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18 Backpropagation (Sensitivities) The sensitivities are computed by starting at the last layer, and then propagating backwards through the network to the first layer.
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19 Initialization (Last Layer) a i n i M ---------- a i M n i M ---------- f M n i M n i M -----------------------f Ý M n i M === s i M 2t i a i – –f Ý M n i M =
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20 Summary Forward Propagation Backpropagation Weight Update
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