Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for high-dimensional sparse data commonly encountered in applications like text classification, word-sense disambiguation, and drug design. These applications involve a large number of examples n as well as a large number of features N , while each example has only s << N non-zero features. This paper presents a Cutting Plane Algorithm for training linear SVMs that provably has training time 0(s,n) for classification problems and o sn log n ))for ordinal regression problems. The algorithm is based on an alternative, but equivalent formulation of the SVM optimization problem. Empirically, the Cutting-Plane Algorithm is several orders of magnitude faster than decomposition methods like svm light for large datasets.
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