### Artificial IntelligenceAIMA Exercises

Construct a support vector machine that computes the xor function. Use values of +1 and –1 (instead of 1 and 0) for both inputs and outputs, so that an example looks like $([-1, 1], 1)$ or $([-1, -1], -1)$. Map the input $[x_1,x_2]$ into a space consisting of $x_1$ and $x_1\,x_2$. Draw the four input points in this space, and the maximal margin separator. What is the margin? Now draw the separating line back in the original Euclidean input space.

Construct a support vector machine that computes the xor function. Use values of +1 and –1 (instead of 1 and 0) for both inputs and outputs, so that an example looks like $([-1, 1], 1)$ or $([-1, -1], -1)$. Map the input $[x_1,x_2]$ into a space consisting of $x_1$ and $x_1\,x_2$. Draw the four input points in this space, and the maximal margin separator. What is the margin? Now draw the separating line back in the original Euclidean input space.

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