Perceptron find weight exercise

Question

I have some difficulties with the following exercise.

There are three different diagrams. If possible, find the perceptron-weights $w_0, w_1,$ and $w_2$ for each of them (the decision surface is clearly divided into two regions, one ”positive” the other one ”negative”).

Solution: for diagram 1 it's obvious that the function is $x_2=x_1$, does it mean that $w_0=0,w_1=-1,w_2=1$?

for diagram 2, the function is $0.7x_1+x_2+1.4=0$, does it mean that $w_0=1.4, w_1=0.7, w_2=1$? If the direction makes any sense here?

for diagram 3, $x_2=|x_1|$, I am not sure how to define weight.

Answer 1

Your solutions for 1 and 2 are correct, since the perceptron's weight vector is perpendicular to the decision boundary.

For diagram 3, there is no solution because the perceptron is a linear classifier (i.e. the decision boundary is always a single line).