Support vector machines (SVMs), though accurate, are not preferred in applications requiring great classification speed, due to the number of support vectors being large. To overcome this problem a primal system and method with the following properties has been devised: (1) it decouples the idea of basis functions from the concept of support vectors; (2) it greedily finds a set of kernel basis functions of a specified maximum size (d.sub.max) to approximate the SVM primal cost function well; (3) it is efficient and roughly scales as O(nd.sub.max.sup.2) where n is the number of training examples; and, (4) the number of basis functions it requires to achieve an accuracy close to the SVM accuracy is usually far less than the number of SVM support vectors.