[Solved] SMAI Homework7-perceptrons defined by the threshold expression

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 h_j and h_k be boolean valued function defined over X. Then h_j is more general than or equal to h_k (written h_{j g} h_k) if and only if

(x X)[h_k(x) = 1 h_j(x) = 1]

That is, any instance of h_k also satisfies h_j.

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]

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