text: This document provides the foundations behind the functionality provided by the @math G library (this https URL), focusing on the basic operations the library provides: subsumption, refinement of directed labeled graphs, and distance similarity assessment between directed labeled graphs. @math G development was initially supported by the National Science Foundation, by the EAGER grant IIS-1551338.
  @cite_5: 
  @cite_37: A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discrete-time linear system, thus is efficiently performed by solving simultaneous linear equations. Our kernel is based on an infinite dimensional feature space, so it is fundamentally different from other string or tree kernels based on dynamic programming. We will present promising empirical results in classification of chemical compounds.
  @cite_31: Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attribute-value data. Only recently have researchers started investigating kernels for structured data. This paper describes how kernel definitions can be simplified by identifying the structure of the data and how kernels can be defined on this structure. We propose a kernel for structured data, prove that it is positive definite, and show how it can be adapted in practical applications.
summary: Another related area is that of kernels for structured representations, which allow the application of techniques such as Support Vector Machines to structured data. Typically, kernels for graphs are based on the idea of finding common substructures between two graphs. For example, @cite_37 present a kernel for graphs based on random walks. @cite_5 also studied how to encapsulate their similarity measure for Description Logics into a kernel. For a survey on kernels for structured data the reader is referred to @cite_31 .