Improved distances for structured data

Abstract

The key ingredient for any distance-based method in machine learning is a proper distance between individuals of the domain. Distances for structured data have been investigated for some time, but no general agreement has been reached. In this paper we use first-order terms for knowledge representation, and the distances introduced are metrics that are defined on the lattice structure of first-order terms. Our metrics are shown to improve on previous proposals in situations where feature equality is important. Furthermore, for one of the distances we introduce, we show that its metric space is isometrically embedable in Euclidean space. This allows the definition of kernels directly from the distance, thus enabling support vector machines and other kernel methods to be applied to structured objects. An extension of the distances to handle sets and multi-sets, and some initial work for higher-order representations, is presented as well.