Question-1
classification
\(\mathbf{w} = \begin{bmatrix}1 \\ 2 \\ 3\end{bmatrix}\) is the weight vector of a linear classifier for a binary classification problem whose labels lie in the set \(\{0, 1\}\). If the bias of the classifier is set to \(0\), which of the following is the equation of the decision boundary for this classifier?
Answer
Solution
The decision boundary for a linear classifier is given by \(\mathbf{w}^{T} \mathbf{x} + b = 0\). Since \(b = 0\), this just becomes \(\mathbf{w}^{T} \mathbf{x} = 0\) which results in \(x_1 + 2x_2 + 3x_3 = 0\).