Editing Support vector machine (section)

{{short description|Set of methods for supervised statistical learning}}
{{Machine learning|Supervised learning}}
In [[machine learning]], '''support vector machines''' ('''SVMs''', also '''support vector networks'''<ref name="CorinnaCortes" />) are [[supervised learning|supervised]] [[Maximum-margin hyperplane|max-margin]] models with associated learning [[algorithm]]s that analyze data for [[Statistical classification|classification]] and [[regression analysis]]. Developed at [[AT&T Bell Laboratories]],<ref name="CorinnaCortes" /><ref>{{Cite book |last=Vapnik |first=Vladimir N. |date=1997 |editor-last=Gerstner |editor-first=Wulfram |editor2-last=Germond |editor2-first=Alain |editor3-last=Hasler |editor3-first=Martin |editor4-last=Nicoud |editor4-first=Jean-Daniel |chapter=The Support Vector method |chapter-url=https://link.springer.com/chapter/10.1007/BFb0020166 |title=Artificial Neural Networks — ICANN'97 |series=Lecture Notes in Computer Science |volume=1327 |language=en |location=Berlin, Heidelberg |publisher=Springer |pages=261–271 |doi=10.1007/BFb0020166 |isbn=978-3-540-69620-9}}</ref> SVMs are one of the most studied models, being based on statistical learning frameworks of [[VC theory]] proposed by [[Vladimir Vapnik|Vapnik]] (1982, 1995) and [[Alexey Chervonenkis|Chervonenkis]] (1974).

In addition to performing [[linear classifier|linear classification]], SVMs can efficiently perform non-linear classification using the [[Kernel method#Mathematics: the kernel trick|''kernel trick'']], 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 [[feature space]]. Thus, SVMs use the kernel trick to implicitly map their inputs into high-dimensional feature spaces, where linear classification can be performed.<ref>{{cite book|last1=Awad|first1=Mariette|last2=Khanna|first2=Rahul|title=Efficient Learning Machines|chapter=Support Vector Machines for Classification|pages=39–66|doi=10.1007/978-1-4302-5990-9_3|doi-access=free|publisher=Apress|isbn=978-1-4302-5990-9|year=2015}}</ref>  Being max-margin models, SVMs are resilient to noisy data (e.g., misclassified examples). SVMs can also be used for [[Regression analysis|regression]] tasks, where the objective becomes <math>\epsilon</math>-sensitive.

The support vector clustering<ref name="HavaSiegelmann">{{cite journal |last1=Ben-Hur |first1=Asa |last2=Horn |first2=David |last3=Siegelmann |first3=Hava |last4=Vapnik |first4=Vladimir N. |title="Support vector clustering" (2001); |journal=Journal of Machine Learning Research |volume=2 |pages=125–137}}</ref> algorithm, created by [[Hava Siegelmann]] and [[Vladimir Vapnik]], applies the statistics of support vectors, developed in the support vector machines algorithm, to categorize unlabeled data.{{Citation needed|date=March 2018}} These data sets require [[unsupervised learning]] approaches, which attempt to find natural [[Cluster analysis|clustering of the data]] 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 [[structured prediction]] problems. It is not clear that SVMs have better predictive performance than other linear models, such as [[logistic regression]] and [[linear regression]].<ref>{{cite journal
 | last1 = Huang
 | first1 = H. H.
 | last2 = Xu
 | first2 = T.
 | last3 = Yang
 | first3 = J.
 | title = Comparing logistic regression, support vector machines, and permanental classification methods in predicting hypertension
 | journal = BMC Proceedings
 | volume = 8
 | issue = Suppl 1
 | pages = S96
 | year = 2014
 | doi = 10.1186/1753-6561-8-S1-S96
 | doi-access = free
 | pmid = 25519351
 | pmc = 4143639
 }}</ref>