A hyperplane is a multi-dimensional linear function that splits space into two distinct regions. In the context of a classifier, it splits feature space into disjunct sub-spaces (one for each class). SVMs effectively place a hyperplane with maximum margin, thereby separating classes in an optimal way.
Worth keeping in mind that though it may be optimal according to some mathematical criterion, that is no guarantee that it's the best for the purposes you have in mind.
Or as the subspace of all the vectors are orthogonal to a given single vector, or as the subspace generated by any orthogonal basis with one base vector removed, or as the kernel of a linear form, ... – but a more visual explanation is probably better as a first foray in the question.
Yeah, but only a few are made up to seem like terms of art designed to obfuscate their actual meaning; and usually prepending "hyper-" to something is a signal that a more clear description of the thing doesn't yet exist.
For 2d, a line, for 3d a plane, for nd a hyperplane.
https://en.wikipedia.org/wiki/Hyperplane
A hyperplane is a multi-dimensional linear function that splits space into two distinct regions. In the context of a classifier, it splits feature space into disjunct sub-spaces (one for each class). SVMs effectively place a hyperplane with maximum margin, thereby separating classes in an optimal way.
Worth keeping in mind that though it may be optimal according to some mathematical criterion, that is no guarantee that it's the best for the purposes you have in mind.
A subspace of dimension n-1 of a n-dimensional vector space. It is an extension of the well-known concept of a 2d-plane in a 3d-space to nd-spaces.
You could also describe a hyperplane as the set of solutions of a system of linear equations.
Or as the subspace of all the vectors are orthogonal to a given single vector, or as the subspace generated by any orthogonal basis with one base vector removed, or as the kernel of a linear form, ... – but a more visual explanation is probably better as a first foray in the question.
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a partition of Euclidean space into two convex sets ;)
it's a word (a made up word)
All words are made up!
Yeah, but only a few are made up to seem like terms of art designed to obfuscate their actual meaning; and usually prepending "hyper-" to something is a signal that a more clear description of the thing doesn't yet exist.
Downvote away, fellas.
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