Question9 Assume that you have to classify the following data and you have decided to use SVM. After training your model you got 4 support vectors which are circled in red, which of the following statements is CORRECT? (select one) By removing any one of non-red circle points from the data, the decision boundary will change By removing any one of red points from the data, the decision boundary will change By removing any point from the data, the decision boundary will change All of the above ResetMaximum marks: 1.5 Flag question undefined单项选择题
A
By removing any one of non-red circle points from the data, the decision boundary will change
B
By removing any one of red points from the data, the decision boundary will change
C
By removing any point from the data, the decision boundary will change
D
All of the above

Question

Question9 Assume that you have to classify the following data and you have decided to use SVM. After training your model you got 4 support vectors which are circled in red, which of the following statements is CORRECT? (select one) By removing any one of non-red circle points from the data, the decision boundary will change By removing any one of red points from the data, the decision boundary will change By removing any point from the data, the decision boundary will change All of the above ResetMaximum marks: 1.5 Flag question undefined单项选择题

A

By removing any one of non-red circle points from the data, the decision boundary will change

B

By removing any one of red points from the data, the decision boundary will change

C

By removing any point from the data, the decision boundary will change

D

All of the above

BlackTom AI · Accepted Answer

Question: After training an SVM, you obtained 4 support vectors (circled in red). Which statement is CORRECT? (select one)

Option 1: By removing any one of non-red circle points from the data, the decision boundary will change
- This is incorrect. Non-support vectors (points not circled) do not affect the position of the decision boundary in an SVM. The boundary is determined by the support vectors and their margins, so removing these non-red points should not change the boundary.

Option 2: By removing any one of red points from the data, the decision boundary will change
- This is correct. Support vectors lie on or near the margin and define the optimal separating hyperplane. If you remove a red (support) vector, especially one that participates in defining the margin, the optimal boundary can shift to reflect the new set of support vectors.

Option 3: By removing any point from the data, the decision boundary will change
- This is incorrect. Not every point in the training set influences the boundary. Only support vectors influence the margin and the decision boundary; removing a non-support vector typically leaves the boundary unchanged.

Option 4: All of the above
- This is incorrect because Options 1 and 3 are not true in general for SVMs, as explained above.

Rationale in brief: In SVMs, the decision boundary is determined by the support vectors—the points that lie closest to the boundary and define the margin. Removing a non-support point does not alter the boundary, while removing a support vector can change which points become support vectors and thus shift the boundary. Therefore, the only statement that correctly captures this is Option 2.