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The soft-margin support vector machine described above is an example of an empirical risk minimization (ERM) algorithm for the hinge loss. Seen this way, support vector machines belong to a natural class of algorithms for statistical inference, and many of its unique features are due to the behavior of the hinge loss.
Consider a binary classification problem with a dataset (x 1, y 1), ..., (x n, y n), where x i is an input vector and y i ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows:
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]
In 2008, she jointly with Vladimir Vapnik received the Paris Kanellakis Award for the development of a highly effective algorithm for supervised learning known as support vector machines (SVM). [10] She was named an ACM Fellow in 2023 for theoretical and practical contributions to machine learning, industrial leadership and service to the field.
Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize ...
In machine learning (ML), a margin classifier is a type of classification model which is able to give an associated distance from the decision boundary for each data sample. For instance, if a linear classifier is used, the distance (typically Euclidean , though others may be used) of a sample from the separating hyperplane is the margin of ...
Support Vector Machine (SVM) classification with a bounded kernel and where the regularizer is a norm in a Reproducing Kernel Hilbert Space. A large regularization constant leads to good stability. [4] Soft margin SVM classification. [4] Regularized Least Squares regression. [4] The minimum relative entropy algorithm for classification. [4]
Margin (machine learning) R. Radial basis function kernel; ... Structured support vector machine This page was last edited on 29 July 2022, at 03:27 (UTC). Text ...