Machine Learning MCQ - Effect of increasing C in soft-margin SVM

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Machine Learning MCQ - Effect of increasing regularization parameter C in soft-margin SVM

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1. In a soft-margin Support Vector Machine (SVM), if we increase C, which of the following are likely to happen?

a) The margin will grow wider

b) Most non-zero slack variables will grow

c) The norm |w| will grow larger        

d) There will be more points inside the margin

Answer: (c) The norm |w| will grow larger The norm of the weight vector w in SVM is inversely related to the margin. The larger C is, the smaller the margin tends to be because the optimization focuses more on minimizing the slack variables than on maximizing the margin. This typically leads to a larger norm of w since it needs to be adjusted more finely to accommodate the penalties introduced by the slack variables.   Why not option (a)? - As the value of C increases, the width of the margin typically decreases, as the model becomes more focused on correctly classifying training samples rather than maximizing the margin. Increase in C value makes the optimization process to focus more on minimizing classification errors. This often leads to a narrower margin, as the model may allow less flexibility in how far the support vectors are from the decision boundary to ensure that most (or all) training points are correctly classified. You will be overfitting the data because SVM will try to classify every point correctly and it cannot be done by increasing the margin.   Why not option (b)? – Most non-zero slack variable will shrink. For points that are already misclassified or have slack variables greater than zero, increasing C forces the optimizer to reduce the slack as much as possible, because the penalty for having non-zero slack increases.   Why not option (d)? - As the value of C increases, the width of the margin typically decreases, and hence we cannot have more points inside the margin.   Difference between soft margin and hard margin Hard margin SVM is applicable for linearly separable data. Soft margin SVM is applicable for non-linear data.

 

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