Question 1

Consider the following dataset: $$D = \left\{\left(\begin{bmatrix} -2 \\ 1 \end{bmatrix}, +1\right), \left(\begin{bmatrix} -1 \\ 1 \end{bmatrix}, +1\right), \left(\begin{bmatrix} -1 \\ -1 \end{bmatrix}, -1\right), \left(\begin{bmatrix} 2 \\ 1 \end{bmatrix}, -1\right)\right\}.$$ The perceptron algorithm is applied on this data set with the weight vector initialized to $\begin{bmatrix} 0 & 0 \end{bmatrix}^T$. Will the algorithm converge after the second round of update of the weight vector? While looking for mistakes, cycle through the data points form left to right. Figure from the original question paper Figure from the original question paper