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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:
For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using inner products.
The training and test-set errors can be measured without bias and in a fair way using accuracy, precision, Auc-Roc, precision-recall, and other metrics. Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a
Least-squares support-vector machines (LS-SVM) for statistics and in statistical modeling, are least-squares versions of support-vector machines (SVM), which are a set of related supervised learning methods that analyze data and recognize patterns, and which are used for classification and regression analysis.
The structured support-vector machine is a machine learning algorithm that generalizes the Support-Vector Machine (SVM) classifier. Whereas the SVM classifier supports binary classification , multiclass classification and regression , the structured SVM allows training of a classifier for general structured output labels .
The basic Support Vector Machine (SVM) paradigm is trained using both positive and negative examples, however studies have shown there are many valid reasons for using only positive examples. When the SVM algorithm is modified to only use positive examples, the process is considered one-class classification. One situation where this type of ...
In machine learning, a ranking SVM is a variant of the support vector machine algorithm, which is used to solve certain ranking problems (via learning to rank). The ranking SVM algorithm was published by Thorsten Joachims in 2002. [1] The original purpose of the algorithm was to improve the performance of an internet search engine.