A Linearly Convergent Linear-Time First-Order Algorithm for Support Vector Classification with a Core Set Result Piyush Kumar Department of Computer Science, Florida State University, Tallahassee, FL 32306-4530, USA, piyush@cs.fsu.edu E. Alper Yıldırım Department of Industrial Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey, yildirim@bilkent.edu.tr We present a simple, first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and ǫ ∈ (0, 1), the proposed algorithm computes a separating hyperplane whose margin is within a factor of (1 − ǫ) of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended to nonlinearly separable and inseparable data sets. The running time of our algorithm is linear in the number of data points and in 1/ǫ. In particular, the number of support vectors computed by the algorithm is bounded above by O(ζ/ǫ) for all sufficiently small ǫ> 0, where ζ is the square of the ratio of the distances between the farthest and closest pairs of points in the two data sets. Furthermore, we establish that our algorithm exhibits linear convergence. Our computational experiments reveal that the proposed algorithm performs quite well on standard data sets in comparison with other first-order algorithms. We adopt the real number model of computation in our analysis. Key words: Support vector machines, support vector classification, Frank-Wolfe algorithm, approximation algorithms, core sets, linear convergence. AMS Subject Classification: 65K05, 90C20, 90C25. History: Submitted April, 2009. Revised February, 2010. 1. Introduction Support vector machines (SVMs) are one of the most commonly used methodologies for classification, regression, and outlier detection. Given a pair of linearly separable data sets P⊂ R n and Q⊂ R n , the support vector classification problem asks for the computation of a hyperplane that separates P and Q with the largest margin. Using kernel functions, the 1