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I'm learning Support Vector Machines, and I'm unable to understand how a class label is chosen for a data point in a binary classifier. Is it chosen by consensus with respect to the classification in each dimension of the separating hyperplane?

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The term consensus, as far as I'm concerned, is used rather for cases when you have more a than one source of metric/measure/choice from which to make a decision. And, in order to choose a possible result, you perform some average evaluation/consensus over the values available.

This is not the case for SVM. The algorithm is based on a quadratic optimization, that maximizes the distance from the closest documents of two different classes, using a hyperplane to make the split.

Hyperplane separating two different classes

So, the only consensus here is the resulting hyperplane, computed from the closest documents of each class. In other words, the classes are attributed to each point by calculating the distance from the point to the hyperplane derived. If the distance is positive, it belongs to a certain class, otherwise, it belongs to the other one.

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