The effectiveness of SVM depends on the selection of kernel, kernel's parameters and soft margin parameter C. A common choice is a gaussian kernel, which has a single parameter? Best combination of C and?
Each pair of parameters is checked using cross validation, and the parameters with best cross validation accuracy are picked. The final model, which is used for testing and classifying new data, is then trained on the whole training set using the selected parameters. Multiclass SVM aims to assign labels to instances by using support vector machines, where the labels are drawn from a finite set of several elements.
The dominating approach for doing so is to reduce the single multiclass problem into multiple binary classification problems. Each of the problems yields a binary classifier, which is assumed to produce an output function that gives relatively large values for examples from the positive class and relatively small values for examples belonging to the negative class.
Two common methods to build such binary classifiers are where each classifier distinguishes between i one of the labels to the rest one-versus-all or ii between every pair of classes one-versus-one. Classification of new instances for one-versus-all case is done by a winner-takes-all strategy, in which the classifier with the highest output function assigns the class it is important that the output functions be calibrated to produce comparable scores.
For the one-versus-one approach, classification is done by a max-wins voting strategy, in which every classifier assigns the instance to one of the two classes, then the vote for the assigned class is increased by one vote, and finally the class with most votes determines the instance classification.
The model produced by support vector classification as described above depends only on a subset of the training data, because the cost function for building the model does not care about training points that lie beyond the margin.
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 reliant on heuristics for breaking the problem down into smaller, more-manageable chunks.
A common method for solving the QP problem 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.
To avoid solving a linear system involving the large kernel matrix, a low rank approximation to the matrix is often used to use the kernel trick. Currently there exist several data science platforms that provide implementation, training, validation and testing for SVM algorithm.
The following are some examples:. From Wikibooks, open books for an open world. The latest reviewed version was checked on 19 February Namespaces Book Discussion. The development of these ideas started in and they were first published in [1]. The support vector SV machine implements the following idea: It maps the input vectors x into a high-dimensional feature space Z through some nonlinear mapping, chosen a priori. In this space, an optimal separating hyperplane is constructed.
The original maximum-margin hyperplane algorithm proposed by Vapnik in constructed a linear classifier. In , Boser, Guyon and Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick to maximum-margin hyperplanes.
The resulting algorithm is formally similar, except that every dot product is replaced by a nonlinear kernel function. This allows the algorithm to fit the maximum-margin hyperplane in a transformed feature space. The transformation may be nonlinear and the transformed space high dimensional; although the classifier is a hyperplane in the transformed feature space, it may be nonlinear in the original input space [7].
Shawe-Taylor, J. Cambridge University Press, Cambridge. Book website: www. Scholkopf, B. Lanckriet, G. Joachims, T. Dumais, S. LeCun, Y. In: Fogelman-Soulie F. EC2 Google Scholar.
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