Kernels over relational algebra structures

Authors:
Adam Woźnica;Alexandros Kalousis;Melanie Hilario
Affiliations:
Computer Science Department, University of Geneva, Geneva 4, Switzerland;Computer Science Department, University of Geneva, Geneva 4, Switzerland;Computer Science Department, University of Geneva, Geneva 4, Switzerland
Venue:
PAKDD'05 Proceedings of the 9th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Year:
2005

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Abstract

In this paper we present a novel and general framework based on concepts of relational algebra for kernel-based learning over relational schema. We exploit the notion of foreign keys to define a new attribute that we call instance-set and we use this type of attribute to define a tree like structured representation of the learning instances. We define kernel functions over relational schemata which are instances of $\Re$-Convolution kernels and use them as a basis for a relational instance-based learning algorithm. These kernels can be considered as being defined over typed and unordered trees where elementary kernels are used to compute the graded similarity between nodes. We investigate their formal properties and evaluate the performance of the relational instance-based algorithm on a number of relational data sets.