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Support vector machines (SVM's) have been introduced in literature as a method for pattern recognition and function estimation, within the framework of statistical learning theory and structural risk minimization. A least squares version (LSSVM) has been recently reported which expresses the training in terms of solving a set of linear equations instead of quadratic programming as for the standard SVM case. In this paper we present an iterative training algorithm for LS-SVM's which is based on a conjugate gradient method. This enables solving large scale classi cation problems which is illustrated on a multi two-spiral benchmark problem.