For this problem, assume that we are training an SVM with a linear kernel and b

Question

For this problem, assume that we are training an SVM with a linear kernel and b quadratic kernel (i.e., our kernel function is a polynomial kernel of degree 2). You are given the data set presented in Figure 1. The slack penalty C will determine the location of the separating hyperplane. Please answer the following questions for both linear kernel and quadratic kernel. Give a one sentence answer justification for each and draw your solution in the appropriate part of the Figure at the end of the problem.

Explanation / Answer

as we can see image and notice that if we draw a vertical line from 0.7 then this line will classify data and moreover

a simple linear kernel might perform kindly enough when the dimensionality of original data is high. Because the data can be seen as linearly separated in such high dimensions, it's no need to map data onto a higher dimensional space by RBF kernel or others.

so in this case we notice that data is well seperated we only need linear classifier only

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