tut7_sol - EE4210 Solution to Tutorial 7 Learning in a 1-D...

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1 EE4210 Solution to Tutorial 7 Learning in a 1-D Self-Organizing Map (a) Initial input x = [ x 1 x 2 x 3 x 4 ] = [0.85 0 0.05 0.1], η = 0.6 Δ w ji ( n ) = [ x i ( n ) - w ji ( n )] for the winning neuron and neurons inside the neigbourhood Δ w ji ( n ) = 0 for all other neurons 1 st iteration ( n =0, neighbourhood size = 1) v 1 (0)= w 11 (0) x 1 + w 12 (0) x 2 + w 13 (0) x 3 + w 14 (0) x 4 = 0.10 v 2 (0)= w 21 (0) x 1 + w 22 (0) x 2 + w 23 (0) x 3 + w 24 (0) x 4 = 0.12 v 3 (0)= w 31 (0) x 1 + w 32 (0) x 2 + w 33 (0) x 3 + w 34 (0) x 4 = 0.70 (the largest output) v 4 (0)= w 41 (0) x 1 + w 42 (0) x 2 + w 43 (0) x 3 + w 44 (0) x 4 = 0.29 Neuron 3 is the winning neuron and it can have its weights updated. Δ w 31 (0) = η [ x 1 (0) - w 31 (0)] = 0.6 [0.85 – 0.82 ] = 0.018 Δ w 32 (0) = [ x 2 (0) - w 32 (0)] = 0.6 [ 0 – 0.1 ] = –0.06 Δ w 33 (0) = [ x 3 (0) - w 33 (0)] = 0.6 [ 0.05 – 0.03 ] = 0.012 Δ w 34 (0) = [ x 4 (0) - w 34 (0)] = 0.6 [ 0.1 – 0.05 ] = 0.03 Δ w 3 (0) = [0.018 –0.06 0.012 0.03] As the neighbourhood size is 1, neurons 2 and 4 can also have their weights updated. Δ
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tut7_sol - EE4210 Solution to Tutorial 7 Learning in a 1-D...

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