In this problem, we will try to understand the convergence of perceptron algorithm and its relation to the ordering of t

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In This Problem We Will Try To Understand The Convergence Of Perceptron Algorithm And Its Relation To The Ordering Of T 1 (128.31 KiB) Viewed 36 times

In this problem, we will try to understand the convergence of perceptron algorithm and its relation to the ordering of the training samples for the following simple example. Consider a set of n = d labeled d-dimensional feature vectors, {(x(t), y(t)), t = 1,..., d} defined as follows: (t) cos (nt) if it (4.7) (t) (4.8) 0 otherwise, = Recall the no-offset perceptron algorithm, and assume that . x = 0 is treated as a mistake, regardless of label. Assume that in all of the following problems, we initialize 0 = 0 and when we refer to the perceptron algorithm we only consider the no-offset variant of it. Working out Perceptron Algorithm 3 points possible (graded) Consider the d = 2 case. Let y(¹) = 1, y(²) = 1. Assume that the feature vector (¹) is presented to the perceptron algorithm before x(2). For this particular assignment of labels, work out the perceptron algorithm until convergence. Let Ô be the resulting value after convergence. Note that for d = 2, Ô would be a two-dimensional vector. Let's denote the first and second components of by ₁ and 2 respectively. Ô Please enter the total number of updates made to by perceptron algorithm: Please enter the numerical value of 11: Please enter the numerical value of 12: x;