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I know how to train a simple competitive network. Let's say I have three inputs $x_1, x_2, x_3$ and learning coefficient $\eta=0.5.$ Let's say I have two neurons $w_1, w_2$. For each input I will compute $\Vert x_i-w_j\Vert^2$ and the smallest distance will define the winner neuron. Then I will update the weight of the winner to $w_j = w_j +\eta(x-w_j)$ .

However, I am not sure how in this simple competitive network, we define the decision boundaries. For example in perceptron I know that i will draw the line $w_1+w_2-b=0$.

For example assume that I have after training:
x1=[1, 1] , class 0
x2= [-1, -1] class 1
x3 = [1, -1] class 0
and
w1 = [1.25, -0.25]
w2 = [-0.5, -2] .

What's the decision boundary?

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Because $x$ will be assigned to the closest $w$, in the end, it'll be just like nearest neighbor boundaries, i.e. voronoi regions around each $w$.

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  • $\begingroup$ is there a practical way to draw this? Because here we only have two classes, instead of n seeds (in voronoi). I cannot just take the a perpedicular to the middle of the line that connects $w_1, w_2$, right? $\endgroup$ Commented Jan 22, 2023 at 16:39
  • $\begingroup$ In case of two $w$, yes you can take the perpendicular line $\endgroup$
    – gunes
    Commented Jan 22, 2023 at 17:45

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