Classification in Non-Metric Spaces

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs. Complex notions of similar(cid:173) ity appear necessary for cognitive models and applications, while simple notions of similarity form a tractable basis for current computational ap(cid:173) proaches to classification. We explore the nature of this dichotomy and why it calls for new approaches to well-studied problems in learning. We begin this process by demonstrating new computational methods for supervised learning that can handle complex notions of similarity.