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Kernels and Distances for Structured Data
Authors:Gärtner  Thomas  Lloyd  John W.  Flach  Peter A.
Affiliation:(1) Fraunhofer Institut Autonome Intelligente Systeme, Germany; Department of Computer Science, University of Bristol, United Kingdom;(2) Department of Computer Science III, University of Bonn, Germany;(3) Research School of Information Sciences and Engineering, The Australian National University, Australia;(4) Machine Learning, Department of Computer Science, University of Bristol, United Kingdom
Abstract:This paper brings together two strands of machine learning of increasing importance: kernel methods and highly structured data. We propose a general method for constructing a kernel following the syntactic structure of the data, as defined by its type signature in a higher-order logic. Our main theoretical result is the positive definiteness of any kernel thus defined. We report encouraging experimental results on a range of real-world data sets. By converting our kernel to a distance pseudo-metric for 1-nearest neighbour, we were able to improve the best accuracy from the literature on the Diterpene data set by more than 10%.
Keywords:kernel methods  structured data  inductive logic programming  higher-order logic  instance-based learning
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