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The original maximum-margin hyperplane algorithm proposed by Vapnik in 1963 constructed a linear classifier. However, in 1992, Bernhard Boser, Isabelle Guyon and Vladimir Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick (originally proposed by Aizerman et al. [20]) to maximum-margin hyperplanes. [7]
The plot shows that the Hinge loss penalizes predictions y < 1, corresponding to the notion of a margin in a support vector machine. In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). [1]
A related result is the supporting hyperplane theorem. In the context of support-vector machines, the optimally separating hyperplane or maximum-margin hyperplane is a hyperplane which separates two convex hulls of points and is equidistant from the two. [1] [2] [3]
So we choose the hyperplane so that the distance from it to the nearest data point on each side is maximized. If such a hyperplane exists, it is known as the maximum-margin hyperplane and the linear classifier it defines is known as a maximum margin classifier.
In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...
Elon Musk shared on X that nor he or Vivek Ramaswamy will be paid to co-lead the newly-created Department of Government Efficiency.
Hence, one should choose the hyperplane such that the distance from it to the nearest data point on each side is maximized. If such a hyperplane exists, it is known as the maximum-margin hyperplane, and the linear classifier it defines is known as a maximum margin classifier (or, equivalently, the perceptron of optimal stability). [citation needed
GM's CFO told investors the company has changed its business strategy to withstand market volatility and a new presidential administration.