University of Florida Optimization Widrow Hoff Learning Questions

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University of Florida

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Assignment - 2 Optimization – Widrow-Hoff Learning Exercise 1 (7 Marks) Consider the following function: 𝟏𝟏 𝑭𝑭(𝐱𝐱) = (𝟏𝟏 + 𝐱𝐱 𝟏𝟏 + 𝐱𝐱 𝟐𝟐 )𝟐𝟐 + 𝐱𝐱 𝟏𝟏𝟒𝟒 𝟒𝟒 1. Find the quadratic approximation to 𝑭𝑭(𝐱𝐱) about the point 𝐱𝐱 0 = [2 2]𝑇𝑇 2. Sketch the contour plot of the quadratic approximation in question 1. 3. Perform one iteration of Newton’s method on the function 𝑭𝑭(𝐱𝐱) from the initial condition x0 given in question 1. Sketch the path from 𝐱𝐱 0 to 𝐱𝐱1 on your contour plot from question 2. 4. Is the 𝐱𝐱1 in question 3 a strong minimum of the quadratic approximation? Is it a strong minimum of the original function? Explain. Exercise 2 (3 Marks) In the following Figure two classes of patterns are given. 1. Use the LMS algorithm to train an ADALINE network to distinguish between class I and class II patterns (we want the network to identify horizontal and vertical lines).
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Optimization – Widrow-Hoff Learning

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Exercise 1
Question 1
F(X) = (1+X1 ...


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