SMAI Homework7-perceptrons defined by the threshold expression Solved

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Consider two perceptrons defined by the threshold expression w0 + w1x1 + w2x2 > 0.

Perceptron A has weight values

w0 = 1,       w1 = 2,       w2 = 1

and Perceptron B has weight values

w0 = 0,w1 = 2,w2 = 1

True or False? Perceptron A is more general than Perceptron B.

Definition: Let hj and hk be boolean valued function defined over X. Then hj is more general than or equal to hk (written hj g hk) if and only if

(∀x X)[hk(x) = 1 → hj(x) = 1]

That is, any instance of hk also satisfies hj.

2        Subjective Question 

Design a two-input perceptron that implements the boolean function A ∧¬B.

3        Programming Question

Using the linear perceptron algorithm, solve the multi-class classification problem of predicting hand-written digit data. Report the accuracy achieved. A starter code has been provided in the ‘Linear Perceptron Excercise.ipynb’ notebook [Hint: You can use a one-vs-one, one-vs-all scheme or use a multi-class signum function]