A binary linear programming formulation of the graph edit distance

A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem. A general formulation for editing graphs is used to derive a graph edit distance that is proven to be a metric, provided...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 28; no. 8; pp. 1200 - 1214
Main Authors: Justice, D., Hero, A.
Format: Journal Article
Language:English
Published: Los Alamitos, CA IEEE 01.08.2006
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Chemicals
Computer Graphics
Computer science; control theory; systems
continuation (homotopy) methods
Cost function
Exact sciences and technology
Fingerprint recognition
Formulations
Graph algorithms
Graphs
graphs and networks
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Information Storage and Retrieval - methods
Information systems
Linear programming
Machine vision
Mathematical models
Operations research
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Polynomials
Product development
Programming, Linear
Prototypes
Recognition
similarity measures
Standards development
structural pattern recognition
Studies
structural pattern recognition
Similarity
Information system
Assignment problem
String matching
Linear programming
Graph theory
Pattern recognition
Continuation method
similarity measures
Homotopy
Chemical databasis
Graph algorithms
continuation (homotopy) methods
Pattern analysis
graphs and networks
Non directed graph
ISSN:0162-8828, 2160-9292, 1939-3539
Online Access:Get full text
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Description
Summary:A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem. A general formulation for editing graphs is used to derive a graph edit distance that is proven to be a metric, provided the cost function for individual edit operations is a metric. Then, a binary linear program is developed for computing this graph edit distance, and polynomial time methods for determining upper and lower bounds on the solution of the binary program are derived by applying solution methods for standard linear programming and the assignment problem. A recognition problem of comparing a sample input graph to a database of known prototype graphs in the context of a chemical information system is presented as an application of the new method. The costs associated with various edit operations are chosen by using a minimum normalized variance criterion applied to pairwise distances between nearest neighbors in the database of prototypes. The new metric is shown to perform quite well in comparison to existing metrics when applied to a database of chemical graphs
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ISSN:0162-8828
2160-9292
1939-3539
DOI:10.1109/TPAMI.2006.152