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As I know the standard linear equation has the following form in $R^2$:

$w_1 x_1 + w_2 x_2 = b$ where $b$ is the intercept with $x_2$

Also I know that a decision boundary in $R^2$ for a perceptron is a line. However I read everywhere that the decision boundary equation is the following:

$w_1 x_1 + w_2 x_2+ b = 0$

Why is that? Shouldn't it be $w_1 x_1 + w_2 x_2 - b = 0$!?

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It probably depends on the exact formulation of the perceptron and its learning algorithm. The decision boundaries are equivalent up to that you need to flip the sign of $b$. Maybe the different references you are looking at do it differently?

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I came across the same issue. It seems its dependent of the literature you are consulting.

w1x1+w2x2−b=0

Seems the correct one, however in some texts, the Bias is already represented as negative (e.g. -2), so the formula is applied as w1x1+w2x2+b=0 which translates to w1x1+w2x2+(-2)=0

Regards,

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