Which points constitute support vectors in SVM without considering regular expressions?

Support vectors in Support Vector Machines (SVM) are specifically defined as the data points that are closest to the separating hyperplane. These points are crucial because they essentially define the position and orientation of the hyperplane that separates different classes in the data.

The intuition behind this is that while many data points can be far from the hyperplane, the support vectors are the ones that actually influence its placement. If you were to remove a support vector, the location of the hyperplane would change, potentially affecting the model's decision boundary.

In contrast, points that are farther from the hyperplane, belong to a certain class, or do not lie on the hyperplane itself, do not contribute directly to the establishment of the decision boundary in the SVM approach. Therefore, understanding that support vectors are precisely those points nearest to the hyperplane helps in grasping how SVM optimally classifies data while minimizing the classification error.