Description
Problem 1 (SVM) – 6 Points: For this problem, you will be investigating the properties of the Support Vector Machine (SVM). The following graph shows points with two possible labels, i.e., + or −.
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(2 points) What is the maximum (hard) margin separating line for the above graph and what is the margin? No need to formally prove that it is the maximum margin, but briefly describe how you know it is maximum.
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(2 points) Is this separating line still optimal when using a soft margin classifier? Why or why not?
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(2 points) We mentioned in class that SVM can be made to generate non-linear classification boundaries as well using the so-called Kernel tricks. In essence, the idea is to transform all points x to φ(x) via a transformation function φ, and the transformed points become separable. To exercise this idea, this question asks you to describe a data transformation in close-form φ(x) : X → V that would allow the data shown in the following graph to become linearly separable (V can be d-dimensional for any d).
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