Inference of Node Replacement Recursive Graph Grammars

1997

1999

2009

This paper is intended as a step towards a theoretically sound approach to learning from graphs, by applying ideas from the field of grammar induction. We present results concerning the learning of hypergraph grammars. We consider identification in the limit from both derivation trees and graphs. We show that, by restricting the complexity of grammars, a learnable class of derivation languages is obtained. By exploiting a known invariance result this class is extended to a class that is learnable from hypergraphs.

2007

This paper describes graph-based relational, unsupervised learning algorithm to infer node replacement graph grammar and its application to metabolic pathways. We search for frequent subgraphs and then check for overlap among the instances of the subgraphs in the input graph. If subgraphs overlap by one node, we propose a node replacement graph grammar production. We also can infer a hierarchy of productions by compressing portions of a graph described by a production and then inferring new productions on the compressed graph. We show learning curves and how the learning process changes when we increase the size of a sample set. We examine how computation time changes with an increased number of nodes in the input graphs. We inferred graph grammars from metabolic pathways which do not change more with increased number of graphs in the input set. It indicates that graph grammars found represent the input sets well.

2009

Many graph mining tasks involve search over languages of graphs. Several approaches to generate graphs exist, but for some applications, however, it is desirable to constrain the search and only consider a subclass of all graphs. For this, the use of language bias has been considered, eg in the field of inductive logic programming. In the context of graph mining, one would expect of a similar general language bias mechanism that it allows one to specify many different classes of graphs in a declarative way.

Theoretical Computer Science, 1982

Fundamenta Informaticae, 2016

Though graph grammars have been widely investigated for 40 years, few learning results exist for them. The main reasons come from complexity issues that are inherent when graphs, and a fortiori graph grammars, are considered. The picture is however different if one considers drawings of graphs, rather than the graphs themselves. E.g., it has recently been proved that the isomorphism and pattern searching problems could be solved in polynomial time for plane graphs, that is, planar embedding of planar graphs. In this paper, we introduce the Plane Graph Grammars (PGG) and detail how they differ to usual graph grammar formalisms while at the same time they share important properties with string context-free grammars. In particular, the parsing of a graph with a given PGG is polynomial for languages with appropriate restrictions. We demonstrate that PGG are well-shaped for learning: we show how recent results on string grammars can be extended to PGG by providing a learning algorithm that identifies in the limit the class of substitutable plane graph languages. Our algorithm runs in polynomial time assuming the same restriction used for polynomial parsing, and the amount of data needed for convergence is comparable to the one required in the case of strings.

1999

Lecture Notes in Computer Science

Regular tree grammars can be used to generate graphs, by generating expressions that denote graphs. Top-down and bottom-up tree transducers are a tool for proving properties of such graph generating tree grammars. graph languages: the HR-context-free and the VR-context-free graph languages. We give some simple examples.

Dagstuhl Seminar Proceedings, 2004

Until now there have been few contributions concerning the verification of graph grammars, specifically of infinite-state graph grammars. This paper compares two existing approaches, based on abstractions of graph transformation systems. While in the unfolding approach graph grammars are approximated by Petri nets, in the partitioning approach graphs are abstracted according to their local structure. We describe differences and similarities of the two approaches and explain the underlying ideas.