Question 1

Consider the two binary images shown below. The white square represents 0 and the black square represents 1. Suppose we use MP neuron to classify these two images by flattening the image of size 5 × 5 into a vector of length 25 × 1. Figure from the original question paper Which of the following threshold *θ* will help the MP neuron classify these two images correctly with the following decision rule? Assume the image of number two belongs to class (1) and the image of number one belongs to class (0) Figure from the original question paper Consider a dataset $$X = \begin{bmatrix} 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 \end{bmatrix}$$ Each column $x_i$ of $X$ represents a data point. The first four data points $(x_1, x_2, x_3, x_4)$ belong to a positive class and the next four data points $(x_5, x_6, x_7, x_8)$ belong to the negative class. The perceptron uses the following decision rule, $$y = \begin{cases} 1, & \text{if } w^T x_i \geq 0 \\ 0, & \text{if } w^T x_i < 0 \end{cases}$$ Based on the above data, answer the given subquestions. Suppose we use the perceptron to classify the data points. The initial weights $w_0$ is given by $w_0 = \sum_{i=1}^{8} x_i$. For each iteration, the algorithm visits a single data point in the following order (that is, $x_1, x_2, x_3, \cdots, x_8$) and updates the weights, if required. Update the weights until the algorithm converges (that is, it classifies all the data points correctly). If the algorithm converges in a finite number of iterations, enter the sum of the elements of the final updated weight vector. If the algorithm doesn't converge, then enter -1. Consider a dataset $$X = \begin{bmatrix} 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 \end{bmatrix}$$ Each column $x_i$ of $X$ represents a data point. The first four data points $(x_1, x_2, x_3, x_4)$ belong to a positive class and the next four data points $(x_5, x_6, x_7, x_8)$ belong to the negative class. The perceptron uses the following decision rule, $$y = \begin{cases} 1, & \text{if } w^T x_i \geq 0 \\ 0, & \text{if } w^T x_i < 0 \end{cases}$$ Based on the above data, answer the given subquestions. The statement that the perceptron update rule works only for Boolean inputs and Boolean output is