In support vector machines (SVM), what are the data points closest to the decision boundary that determine the margin width called?

In support vector machines (SVM), the data points that are closest to the decision boundary and play a crucial role in defining the margin width are known as support vectors. These points are significant because they are the ones that are most difficult to classify, and they directly influence the position and orientation of the decision boundary.

The concept of the margin is fundamental to SVMs; it refers to the distance between the decision boundary and the nearest data points from either class. The support vectors are the data points that lie on the edge of the margin and dictate the size of this margin. If the support vectors were to change, the decision boundary might shift, resulting in a different classification of the data points.

In contrast, other terms like "decision points," "margin points," and "boundary vectors" are not standard terminology used in the context of SVMs and do not convey the specific role that support vectors play in the model. Thus, recognizing support vectors is essential for understanding how SVM operates, making this answer the most appropriate.