# How can I draw the decision boundary for a simple competitive network?

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?

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 $$w$$.
• 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? Commented Jan 22, 2023 at 16:39
• In case of two $w$, yes you can take the perpendicular line Commented Jan 22, 2023 at 17:45