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Sparse support vector machine (SVM) is a popular classification techniquethat can simultaneously learn a small set of the most interpretable featuresand identify the support vectors. It has achieved great successes in manyreal-world applications. However, for large-scale problems involving a hugenumber of samples and ultra-high dimensional features, solving sparse SVMsremains challenging. By noting that sparse SVMs induce sparsities in bothfeature and sample spaces, we propose a novel approach, which is based onaccurate estimations of the primal and dual optima of sparse SVMs, tosimultaneously identify the inactive features and samples that are guaranteedto be irrelevant to the outputs. Thus, we can remove the identified inactivesamples and features from the training phase, leading to substantial savings inthe computational cost without sacrificing the accuracy. Moreover, we show thatour method can be extended to multi-class sparse support vector machines. Tothe best of our knowledge, the proposed method is the \emph{first}\emph{static} feature and sample reduction method for sparse SVMs andmulti-class sparse SVMs. Experiments on both synthetic and real data setsdemonstrate that our approach significantly outperforms state-of-the-artmethods and the speedup gained by our approach can be orders of magnitude.

Scaling Up Sparse Support Vector Machines by Simultaneous Feature and Sample Reduction