In the following featured diagram, which line is most likely to be selected by SVM as the decision boundary that classifies the two classes (crosses vs. dots)?

Question

BlackTom AI · Accepted Answer

To determine which line SVM would most likely select as the decision boundary, we start by considering the core principle: a support vector machine chooses the separating hyperplane that maximizes the margin between the two classes.

Option A (the red line): This line appears farther from one side of the data but likely does not maximize the distance to the closest points on both sides; it may also be closer to one class, resulting in a smaller margin and potential misclassification near the margin boundaries.

Option B (the green line): This line sits between the two clusters in a way that keeps the two classes on opposite sides with the greatest possible gap. The dashed parallel lines illustrating the margin around this boundary are visually the widest among the shown candidates, indicating the maximum margin objective is most closely satisfied here. This aligns with SVM’s goal of maximizing margin.

Option C (the blue line): While this line may separate the clusters, its proximity to several datapoints on one side reduces the margin. A smaller margin increases vulnerability to misclassification on new data and is not consistent with the SVM objective depicted by the dashed margin lines.

Option D (the purple line): Although this line may create separation, it runs too close to many support vectors and yields a narrower margin compared to the green line. SVM would favor the line with the larger margin, not this tighter fit.

In summary, the chosen boundary by SVM would be the one that affords the widest margin while correctly separating the two classes; among the options, that is option B.

BU.330.780.T1.SP25 Quiz 2- Requires Respondus LockDown Browser

In the following featured diagram, which line is most likely to be selected by SVM as the decision boundary that classifies the two classes (crosses vs. dots)?

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