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We want to train a perceptron network using the following training set:starting from the initial conditionsi. Sketch the initial decision boundary, and show the weight vector and the three training...

The symmetric hard limit function is sometimes used in perceptron networks, instead of the hard limit function. Target values are then taken from the set [-1, 1] instead of [0, 1].i. Write a simple...

Consider again the four-category classification problem described in Problems P4.3 and P4.5. Suppose that we change the input vector p3 toi. Is the problem still linearly separable? Demonstrate your...

1. Consider the set of all continuous functions that satisfy the condition ƒ(0) = 0. Show that this is a vector space.2. Show that the set of 2 × 2 matrices is a vector space.

One variation of the perceptron learning rule iswhere  is called the learning rate. Prove convergence of this algorithm. Does the proof require a limit on the learning rate? Explain.

Consider the single-neuron perceptron network shown in Figure P5.1. Recall from Chapter 3 (see Eq. (3.6)) that the decision boundary for this network is given by Wp + b =0. Show that the decision...