From support vector machine learning to the determination of the minimum enclosing zone

The verification of form tolerances requires the determination of the minimum enclosing zone according to the ANSI Y14.5M National Standard on Dimensioning and Tolerancing. However, to date many coordinate measuring machines (CMMs) still employ the least-squares method, which has the economic disadvantage of sometimes rejecting good parts. Support vector machines represent a new approach in the area of machine learning, which has been implemented successfully in pattern recognition and regression estimation problems. This article outlines, how the support vector algorithm, as used in classification problems, can be modified in order to identify the minimum enclosing zone for straightness and flatness tolerances. A gradient ascent approach is proposed to identify the solution of the resulting non-convex optimization problem. Numerical results for evaluating the minimum enclosing zone suggest rather promising properties of the employed gradient ascent method.