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Lawrence B. Holder (University of Texas at Arlington, USA)

Copyright: © 2009
|Pages: 7

DOI: 10.4018/978-1-60566-010-3.ch146

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Top*Graph-based data mining* represents a collection of techniques for mining the relational aspects of data represented as a graph. Two major approaches to graph-based data mining are *frequent subgraph mining* and *graph-based relational learning*. This chapter will focus on one particular approach embodied in the Subdue system, along with recent advances in graph-based supervised learning, graph-based hierarchical conceptual clustering, and graph-grammar induction.

Most approaches to data mining look for associations among an entity’s attributes, but relationships between entities represent a rich source of information, and ultimately knowledge. The field of *multi-relational data mining*, of which graph-based data mining is a part, is a new area investigating approaches to mining this relational information by finding associations involving multiple tables in a relational database. Two main approaches have been developed for mining relational information: logic-based approaches and graph-based approaches.

Logic-based approaches fall under the area of *inductive logic programming* (ILP). ILP embodies a number of techniques for inducing a logical theory to describe the data, and many techniques have been adapted to multi-relational data mining (Dzeroski & Lavrac, 2001; Dzeroski, 2003). Graph-based approaches differ from logic-based approaches to relational mining in several ways, the most obvious of which is the underlying representation. Furthermore, logic-based approaches rely on the prior identification of the predicate or predicates to be mined, while graph-based approaches are more data-driven, identifying any portion of the graph that has high support. However, logic-based approaches allow the expression of more complicated patterns involving, e.g., recursion, variables, and constraints among variables. These representational limitations of graphs can be overcome, but at a computational cost.

Graph-based data mining (GDM) is the task of finding novel, useful, and understandable graph-theoretic patterns in a graph representation of data. Several approaches to GDM exist based on the task of identifying frequently occurring subgraphs in graph transactions, i.e., those subgraphs meeting a minimum level of support. Washio and Motoda (2003) provide an excellent survey of these approaches. We here describe four representative GDM methods.

Kuramochi and Karypis (2001) developed the FSG system for finding all frequent subgraphs in large graph databases. FSG starts by finding all frequent single and double edge subgraphs. Then, in each iteration, it generates candidate subgraphs by expanding the subgraphs found in the previous iteration by one edge. In each iteration the algorithm checks how many times the candidate subgraph occurs within an entire graph. The candidates, whose frequency is below a user-defined level, are pruned. The algorithm returns all subgraphs occurring more frequently than the given level.

Yan and Han (2002) introduced gSpan, which combines depth-first search and lexicographic ordering to find frequent subgraphs. Their algorithm starts from all frequent one-edge graphs. The labels on these edges together with labels on incident vertices define a code for every such graph. Expansion of these one-edge graphs maps them to longer codes. Since every graph can map to many codes, all but the smallest code are pruned. Code ordering and pruning reduces the cost of matching frequent subgraphs in gSpan. Yan and Han (2003) describe a refinement to gSpan, called CloseGraph, which identifies only subgraphs satisfying the minimum support, such that no supergraph exists with the same level of support.

Inokuchi et al. (2003) developed the Apriori-based Graph Mining (AGM) system, which searches the space of frequent subgraphs in a bottom-up fashion, beginning with a single vertex, and then continually expanding by a single vertex and one or more edges. AGM also employs a canonical coding of graphs in order to support fast subgraph matching. AGM returns association rules satisfying user-specified levels of support and confidence.

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