Pattern Recognition Theory and Applications pp 323-345 | Cite as

# Structural Pattern Recognition: A Random Graph Approach

## Abstract

This paper presents the notion of random graphs and their associated probability distributions. It addresses both the structural and probabilistic aspects of structural pattern recognition. A structural pattern can be explicitly represented in the form of attributed graphs and an ensemble of such representations can be considered as outcomes of a mapping, called random graph mapping. To account for the variation of structural patterns in the ensemble, a lower order probability distribution is used to approximate the high order joint probability. To synthesize an ensemble of attributed graphs into a probability distribution (or a set of distributions) of a random graph, we introduce a distance measure together with a hierarchical clustering algorithm. The distance measure is defined as the minimum change of a specially defined Shannon’s entropy before and after the merging of the distributions. With this new formulation, both supervised and unsupervised classification of structural patterns can be achieved.

### Keywords

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### References

- [1]Wong, A.K.C. and Goldfarb, L., 1978, “Modeling Systems and Multilevel Hierarchical Relational Structures,” in Savage, G.J. and Roe, P.H., ed., Large
*Engineering Systems*2, Sanford Educational Press, Waterloo, Ontario, pp. 37–44.Google Scholar - [2]Tsai, W.H. and Fu, K.S., 1979, “Error-Correcting Isomorphism of Attributed Relational Graphs for Pattern Analysis”,
*IEEE Trans, on Systems, Man and Cybernetics*, vol. SMC-13, pp. 353–362.MathSciNetGoogle Scholar - [3]Wong, A.K.C. and You, M.L., 1986, “Entropy and Distance of Random Graphs with Application to Structural Pattern Recognition,”
*IEEE Trans, on Pattern Analysis and Machine Intelligence*, vol. PAMI-7, pp. 599–609.CrossRefGoogle Scholar - [4]Shaw, A.C., 1969, “A Formal Picture Description Scheme as a Basis for Picture Processing Systems,”
*Information and Control*, vol. 14, pp. 9–52.MATHCrossRefGoogle Scholar - [5]Shaw, A.C., 1970, “Parsing of Graph-Represent able Pictures,” Journal of ACM, vol. 17, pp. 453–481.MATHCrossRefGoogle Scholar
- [6]Pavlidis, T., 1977,
*Structural Pattern Recognition*, Springer-Verlag.MATHGoogle Scholar - [7]Pavlidis, T., 1980, “Structural Description and Graph Grammars,” in Chang, S.K. and Fu, K.S., ed.,
*Pictorial Information Systems*, Springer-Verlag, pp. 86–103.CrossRefGoogle Scholar - [8]Sanfeliu, A. and Fu, K.S., 1983, “A Distance Measure Between Attributed Relational Graphs for Pattern Recognition,”
*IEEE Trans, on Systems*, Man,*and Cybernetics*, vol. SMC-13, pp. 353–362.Google Scholar - [9]Wong, A.K.C. and Ghahraman, D.E., 1980, “Random Graphs: Structural- Contextual Dichotomy,”
*IEEE Trans. Pattern Analysis and Machine Intelligence*, vol. PAMI-2, pp. 341–348.CrossRefGoogle Scholar - [10]Ghahraman, D.E., Wong, A.K.C. and AU, T., 1980, “Graph Optimal Monomor- phism Algorithms,”
*IEEE Trans, on Systems, Man and Cybernetics*, vol. SMC-10, pp. 189–196.Google Scholar - [11]Shapiro, L.G. and Haralick, R.M., 1981, “Structural Descriptions and Inexact Matching,”
*IEEE Trans, on Pattern Analysis and Machine Intelligence*, vol. PAMI-3, pp. 504–519.CrossRefGoogle Scholar - [12]Ghahraman, D.E., Wong, A.K.C. and Au, T., 1980, “Graph Monomorphism Algorithm,”
*IEEE Trans, on Syst., Man Cybern*., vol. SMC-10, pp. 181–196.CrossRefGoogle Scholar - [13]You, M.L. and Wong, A.K.C., 1984, “An Algorithm for Graph Optimal Isomorphsim,”
*Proc. of the Seventh International Conference on Pattern Recognition*, pp. 316–319.Google Scholar - [14]Masumi, A.E., 1973, Picture Analysis of Graph Transformation, Ph.D. Thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign.Google Scholar
- [15]Fu, K.S., 1980, “Picture Syntax,” in Chang, S.K. and Fu, K.S., ed.,
*Pictorial Information Systems*, Springer-Verlag, pp. 104–127.CrossRefGoogle Scholar - [16]Niemann, H., 1980, “Hierarchical Graphs in Pattern Analysis,”
*Proc. 1980 Int. Conf. on Pattern Recognition*, pp. 213–216.Google Scholar - [17]You, M., 1983, A Random Graph Approach to Pattern Recognition, Ph. D. Thesis, Dept. of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, pp. 37–44.Google Scholar
- [18]Wong, A.K.C., Reichert, T.A., Cohen, D.N., and Aygun, B.O., 1974, “A Generalized Method for Matching Informational Macromolecular Code Sequences,”
*Com- put. Biol. Med*., vol. 4, pp. 43–57.CrossRefGoogle Scholar - [19]Cohen, D.N., Reichert, T.A., and Wong, A.K.C., 1975, “Matching Code Sequences Utilizing Context Free Quality Measures,”
*Mathematical Biosciences*, vol. 24, pp. 25–30.MathSciNetMATHCrossRefGoogle Scholar - [20]Fu, K.S., 1983, “A Step Towards Unification of Syntactic and Statistic Pattern Recognition,”
*IEEE Trans. on Pattern Analysis and Machine Intelligence*, vol PAMI-5, pp. 200–205.Google Scholar - [21]Abe, K. and Sugita, N., 1982, “Distance between Strings of Symbols — Review and Remarks,”
*Proc. 1982 Int. Conf. on Pattern Recognition*, vol. 1, pp. 172–174.Google Scholar - [22]Fu, K.S., 1982,
*Syntactic Pattern Recognition and Applications*, Prentice-Hall.MATHGoogle Scholar