Geometry-Based Learning Algorithms

We present CHILS , the Convex Hull Inductive Learning System, a novel supervised learning algorithm based on approximating concepts with sets of convex hulls. We introduce a theoretical methodology for describing the power of a concept representation language and use it to compare convex hulls with other geometrical concept representations. The Domain Transform framework (DT) provides a clear way to compare the power of supervised learning systems, allowing us to characterize a class of domains which is learnable by some systems but cannot be learned by other systems. DT can be used similarly to compare the expected generalization performance of different domains.