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Training algorithms for radial basis function Kernel classifiers (RBFKCs), such as the canonical support vector machine (SVM), often produce computationally burdensome classifiers when large training data sets are used. Additionally, this complexity is not directly controllable by the developer. A least-squares variant of the SVM is used as a starting point for a proposed algorithm called the incremental asymmetric proximal support vector machine (IAPSVM). IAPSVM employs a greedy search method across the training data to select the centers of each RBF transform. This iterative building process produces a final classifier that compares favorably with both the SVM and another available complexity reduction algorithm (as measured by the number of RBF kernel transforms that must be evaluated to classify an unknown sample). Unlike SVM methods, IAPSVM enables an a priori decision for the complexity of the classifier. This capability is often important for developers when building RBFKCs for resource-constrained systems.