# Support Vector Machine (SVM) Training System

A Support Vector Machine (SVM) Training System is a model training system that can solve an SVM Training Task by implementing an SVM training algorithm.

**AKA:**SVM Software Package.**Context:**- It can range from being a: SVM Classification System to being a SVM Ranking System to being a SVM Regression System.

**Example(s):****Counter-Example(s):****See:**Software Package, Hierarchical SVMs, Eager Model-based Training.

## References

### 2018

- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Support_vector_machine Retrieved:2018-4-8.
- In machine learning,
**support vector machines**(**SVMs**, also**support vector networks**^{[1]}) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. Given a set of training examples, each marked as belonging to one or the other of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier (although methods such as Platt scaling exist to use SVM in a probabilistic classification setting). An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall.In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

When data are not labeled, supervised learning is not possible, and an unsupervised learning approach is required, which attempts to find natural clustering of the data to groups, and then map new data to these formed groups. The

**support vector clustering**^{[2]}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, and is one of the most widely used clustering algorithms in industrial applications.

- In machine learning,

### 2017

- (Zhang, 2017) ⇒ Zhang X. (2017) Support Vector Machines. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA
- QUOTE: Support vector machines (SVMs) are a class of linear algorithms which can be used for classification, regression, density estimation, novelty detection, etc. In the simplest case of two-class classification, SVMs find a hyperplane that separates the two classes of data with as wide a margin as possible. This leads to good generalization accuracy on unseen data and supports specialized optimization methods that allow SVM to learn from a large amount of data.

### 2012

- http://en.wikipedia.org/wiki/Support_vector_machine#Implementation
- The parameters of the maximum-margin hyperplane are derived by solving the optimization. There exist several specialized algorithms for quickly solving the QP problem that arises from SVMs, mostly relying on heuristics for breaking the problem down into smaller, more-manageable chunks.
A common method is Platt's Sequential Minimal Optimization (SMO) algorithm, which breaks the problem down into 2-dimensional sub-problems that may be solved analytically, eliminating the need for a numerical optimization algorithm.

Another approach is to use an interior point method that uses Newton-like iterations to find a solution of the Karush–Kuhn–Tucker conditions of the primal and dual problems.

^{[3]}Instead of solving a sequence of broken down problems, this approach directly solves the problem as a whole. To avoid solving a linear system involving the large kernel matrix, a low rank approximation to the matrix is often used in the kernel trick.

- The parameters of the maximum-margin hyperplane are derived by solving the optimization. There exist several specialized algorithms for quickly solving the QP problem that arises from SVMs, mostly relying on heuristics for breaking the problem down into smaller, more-manageable chunks.

- ↑ Cortes, Corinna; Vapnik, Vladimir N. (1995). “Support-vector networks". Machine Learning. 20 (3): 273–297. doi:10.1007/BF00994018.
- ↑ Ben-Hur, Asa; Horn, David; Siegelmann, Hava; and Vapnik, Vladimir N.; "Support vector clustering"; (2001);
*Journal of Machine Learning Research*, 2: 125–137 - ↑ Ferris, Michael C.; and Munson, Todd S. (2002). "Interior-point methods for massive support vector machines".
*SIAM Journal on Optimization***13**(3): 783–804. doi:10.1137/S1052623400374379.

### 2011

- (Chang et al., 2011) ⇒ Chih-Chung Chang, and Chih-Jen Lin. (2011). “LIBSVM: A Library for Support Vector Machines.” In: ACM Transactions on Intelligent Systems and Technology (TIST) Journal, 2(3). doi:10.1145/1961189.1961199