Support vector machine

In <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a>, support vector machines (SVMs, also support vector networks) are <a href="/facts/Supervised_learning/JlNFNPFt">supervised</a> <a href="/facts/Maximum-margin_hyperplane/9EdtJ3oh">max-margin</a> models with associated learning <a href="/facts/Algorithm/fnl5NmRt">algorithms</a> that analyze data for <a href="/facts/Statistical_classification/jXXHRkXR">classification</a> and <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a>. Developed at <a href="/facts/AT%2526T_Bell_Laboratories/fKP5Gk0H">AT&T Bell Laboratories</a>, SVMs are one of the most studied models, being based on statistical learning frameworks of <a href="/facts/VC_theory/jDST0Ulo">VC theory</a> proposed by <a href="/facts/Vladimir_Vapnik/UQfpyUuN">Vapnik</a> (1982, 1995) and <a href="/facts/Alexey_Chervonenkis/EAgIkPrg">Chervonenkis</a> (1974).
In addition to performing <a href="/facts/Linear_classifier/vsE823wQ">linear classification</a>, SVMs can efficiently perform non-linear classification using the <a href="/facts/Kernel_method/fYuURIPk">kernel trick</a>, representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel function, which transforms them into coordinates in a higher-dimensional <a href="/facts/Feature_space/nzAhYxfu">feature space</a>. Thus, SVMs use the kernel trick to implicitly map their inputs into high-dimensional feature spaces, where linear classification can be performed. Being max-margin models, SVMs are resilient to noisy data (e.g., misclassified examples). SVMs can also be used for <a href="/facts/Regression_analysis/n6z5Tf7K">regression</a> tasks, where the objective becomes 
 
 
 
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The support vector clustering algorithm, created by <a href="/facts/Hava_Siegelmann/pCCqR1CV">Hava Siegelmann</a> and <a href="/facts/Vladimir_Vapnik/UQfpyUuN">Vladimir Vapnik</a>, applies the statistics of support vectors, developed in the support vector machines algorithm, to categorize unlabeled data. These data sets require <a href="/facts/Unsupervised_learning/8a6f61MC">unsupervised learning</a> approaches, which attempt to find natural <a href="/facts/Cluster_analysis/HUeDnWPt">clustering of the data</a> into groups, and then to map new data according to these clusters.
The popularity of SVMs is likely due to their amenability to theoretical analysis, and their flexibility in being applied to a wide variety of tasks, including <a href="/facts/Structured_prediction/hqe45TQD">structured prediction</a> problems. It is not clear that SVMs have better predictive performance than other linear models, such as <a href="/facts/Logistic_regression/mGj6mc8y">logistic regression</a> and <a href="/facts/Linear_regression/5n998IhK">linear regression</a>.

Support vector machine open-in-new

Support vector machine