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Consider a two-dimensional feature space in which the line $\mathbf{w}.\mathbf{x} + b = 0$, where $ \mathbf{w},\mathbf{x} \in \mathbb{R}^ 2 $ and $b \in \mathbb{R}$, separates linearly separable data with labels $y = 0$ and $y = 1$. Suppose the data is such that all points satisfying $\mathbf{w}.\mathbf{x} + b > 0$ have labels $y = 1$ and all points satisfying $\mathbf{w}.\mathbf{x} + b < 0$ have labels $y = 0$. Consider the following two decisions.

Decision 1:

$\mathbf{w}.\mathbf{x} + b > 0 \Rightarrow y = 1 \ \ \& \ \ \mathbf{w}.\mathbf{x} + b < 0 \Rightarrow y = 0.$

Decision 2:

$\mathbf{w}.\mathbf{x} + b > 0 \Rightarrow y = 0 \ \ \& \ \ \mathbf{w}.\mathbf{x} + b < 0 \Rightarrow y = 1.$

Decision 1 gives 100% accuracy and Decision 2 gives 0% accuracy. Hence, in a general setting, should both the decisions be considered and the one that gives a higher accuracy be selected ?

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