Why inside this ellipse y = 1?


[image comes from Decision Boundary 09:35]

I think inside this ellipse y should equals 0 rather than 1,because only when wx+b greater or equals to 0 , can y equals one.

From the previous example shown on 08:30, I can see that outside the boundary circle y=1, and inside the boundary circle y = 0.

Can anybody help me with this question? Thank you so much!!

Which side of the curve has the higher values depends on the sign of the weights.

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For example, if w_1 = w_2 = -1 and b = 1 then y_{hat} = 1 when -x_1^2 - x_2^2 + 1\geq 0 \Leftrightarrow x_1^2 + x_2^2\leq 1. That will be the case inside of the circle, the predictions are going to be 1 instead of 0

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Nice example @sonnh1902. Or if we consider the origin point, then z = b and y_hat = 1 if b > 0. Definitely your argument is more complete.

Cheers,
Raymond

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It would have been easy for the students to follow, if the examples used similar weights.