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The kernel trick, where dot products are replaced by kernels, is easily derived in the dual representation of the SVM problem. This allows the algorithm to fit the maximum-margin hyperplane in a transformed feature space. The transformation may be nonlinear and the transformed space high-dimensional; although the classifier is a hyperplane in ...
Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBoost, for instance) then a sample with a higher margin will receive less (or equal) weight than a sample with a lower margin. This leads the boosting algorithm to focus weight on low-margin samples.
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
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]
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 particular, support vector machines find a hyperplane that separates the feature space into two classes with the maximum margin. If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension ...
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]
Support Vector Machine (SVM): a set of methods which divide multidimensional data by finding a dividing hyperplane with the maximum margin between the two sets Structured SVM: allows training of a classifier for general structured output labels. Winnow algorithm: related to the perceptron, but uses a multiplicative weight-update scheme