Learning class regions by the union of ellipsoids

In many classification schemes objects are represented as points in multi-dimensional feature spaces. The classification scheme then attempts to discriminate between regions in the space occupied by objects of different classes. The performance of the classification method often depends on the shape of the class regions, e.g., whether or not they are linearly separable. In many practical cases, class regions have the structure of smooth low-dimensional manifolds. We develop a novel classification scheme that covers each class region by a set of ellipsoids that are oriented along the local orientation of the manifold. The scheme learns the class regions from sequential presentation of samples, and the ellipsoids are created and modified incrementally during the learning. In high dimensional feature spaces the ellipsoids cover can become significantly more efficient than alternative classification schemes