Which of the following satisfies the support vectors? Suppose the linear model,
ℎ
, is known, and the true label
𝑦
is in
{
−
1
,
1
}
.

Question

Which of the following satisfies the support vectors? Suppose the linear model, 
ℎ
, is known, and the true label 
𝑦
 is in 
{
−
1
,
1
}
.

BlackTom AI · Accepted Answer

In the context of Support Vector Machines with a hard margin, the support vectors are the samples that lie exactly on the margin. For a binary classification with labels y in {−1, 1} and a decision function h(x) that outputs the predicted label sign, the margin condition for a support vector is y * h = 1 (i.e., the product of the true label and the classifier's output is positive and has magnitude 1 on the margin).

To break this down:  y ∈ {−1, 1} indicates the correct class, and h represents the decision function value (often the signed distance to the separating hyperplane, or its sign corresponding to the predicted class). When a sample is exactly at the margin, the classifier's output is scaled so that its confidence exactly meets the margin, which yields y * h = 1.

Therefore, among the possible characterizations of support vectors, the condition y * h = 1 correctly identifies those samples lying on the margin and thus being support vectors in the hard-margin SVM setting. If a point had y * h > 1, it would lie outside the margin and would not be a support vector; if y * h < 1, it would be inside the margin and either misclassified or soft-margin violating, depending on the setup. In the soft-margin variant, support vectors can also occur with y * h in [0, 1], but the classic margin-support-vector condition remains y * h = 1 for the boundary points themselves.

Machine Learning: Fundamentals and Applications Quiz 7 SVM

Which of the following satisfies the support vectors? Suppose the linear model, ℎ , is known, and the true label 𝑦 is in { − 1 , 1 } .

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