# Journal of Advances in Applied Mathematics

### On Sparsity of Soft Margin Support Vector Machines

Download PDF (457.4 KB) PP. 109 - 114 Pub. Date: July 31, 2017

### Author(s)

**Jochen Merker**^{*}

Faculty of Computer Science, Mathematics and Natural Sciences, University of Applied Sciences Leipzig, Germany

### Abstract

*N*of training data and the dimension

*D*of the feature space, it either is advantageous to solve the primal problem or the dual problem. In this article, the case

*D*>>

*N*is discussed where

*D*is so large that even a calculation of the dot product of fully occupied vectors in dimension

*D*is too slow for the desired (e.g. real-time) application. Then a way to speed up the classification is to use an SVM which constructs a sparse linear classifier by solving an optimization problem involving the 1-norm, i.e. many components of the classifying vector are zero so that much less than

*D*multiplications are neccessary to calculate the dot product. For a soft-margin SVM, in this article a theorem on the number of non-zero components is shown.

### Keywords

### References

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