What does the word “support” mean in the context of Vector Machine support, which is a supervised learning model?
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Hyper-margin with maximum margin and margins for SVM trained with samples from two classes. Samples at the edge are called reference vectors.
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The core can be infinite. But as long as you can calculate the similarity of the kernel with the support vectors, you can check which side of the hyperplane the object is on, not knowing what this infinite-dimensional hyperplane looks like.
In 2d, you could, of course, just write the equation for the hyperplane. But this does not provide any real benefits other than understanding SVM.