tut7 - • 1 st iteration : the neighborhood size is set to...

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EE4210 Tutorial 7 Learning in a 1-D Self-Organizing Map Consider the 1-D self-organizing map (SOM) shown in Fig. 1. x i = i th input signal w ji = synaptic weight from input i to neuron j v j = net activity level of neuron j y j = output of neuron j = ϕ ( v j ) = + 1 0 for winning neuron for other neurons η = 0.6 Initial output y = [ y 1 y 2 y 3 y 4 ] = [0 0 0 0] Initial weight = 26 . 0 24 . 0 2 . 0 3 . 0 05 . 0 03 . 0 1 . 0 82 . 0 44 . 0 08 . 0 4 . 0 08 . 0 9 . 0 05 . 0 04 . 0 01 . 0 W(0) Fig. 1 1-D SOM Find the synaptic weights after 2 iterations for the following 2 cases. (a) Initial input x = [ x 1 x 2 x 3 x 4 ] = [0.85 0 0.05 0.1], the winning neuron is defined as the one with the largest v j . (b) Initial input x = [ x 1 x 2 x 3 x 4 ] = [0.1 0.5 0 0.4], the winning neuron is defined as the one with the minimum absolute difference between the input and the weight vector.
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Unformatted text preview: • 1 st iteration : the neighborhood size is set to 1, i.e., h j,i ( x ) of the winning neuron and the two neurons (one at each side) immediately next to it equals to 1. It is zero for all other neurons. • 2 nd iteration : the neighborhood size is reduced to 0, i.e., h j,i ( x ) of the winning neuron is 1 while it is zero for all other neurons. Remark : The neighborhood relationship is NOT cyclic. This means that if the winning neuron is at the end of the 1-D SOM, only one side of neighborhood is considered. w 44 w 14 w 34 x 4 x 3 x 2 x 1 w 41 w 21 w 11 y 1 y 2 1 y 3 2 3 y 4 4...
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