For this problem, assume that we are training an SVM with a linear kernel and b
ID: 3819921 • Letter: F
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
SOLUTION: For large values of C, the penalty for misclassifying points is very high,
so the decision boundary will perfectly separate the data if possible.
See below for the boundary learned using libSVM and C = 100000.
Following are the common mistakes made while drawing .kindly check it
COMMON MISTAKE 1: Some drew straight lines, which would not be the result with a quadratic kernel.
COMMON MISTAKE 2: Some confused the effect of C and thought that a large C meant that the algorithm would be more tolerant of
misclassifications.
=> The classifier can maximize the margin between most of the points,while misclassifying a few points, because the penalty is so low.
See below for the boundary learned by libSVM with C = 0.00005.
=> We were warned not to trust any specific data point too much, so we prefer the solution where C 0, because it maximizes the margin
between the dominant clouds of points.
=> We add the point circled below, which is correctly classified by the original classifier, and will not be a support vector.
=> Since C is very large, adding a point that would be incorrectly classified by the original boundary will force the boundary to move.
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