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Graph edit distance from spectral seriation.

A Robles-Kelly, E R Hancock

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |March 8, 2005
    PubMed
    Summary
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    This study introduces a novel graph edit distance computation method by converting graphs into string sequences. This approach enhances rigor and enables graph matching using sequence alignment techniques for improved clustering.

    Area of Science:

    • Graph theory
    • Computer science
    • Data analysis

    Background:

    • Existing graph edit distance methods lack the formality of string edit distance.
    • There is a need for more rigorous and computationally efficient graph matching techniques.

    Purpose of the Study:

    • To develop a formal method for computing graph edit distance.
    • To adapt string matching techniques for graph comparison.
    • To improve graph clustering by utilizing a novel edit distance.

    Main Methods:

    • Graphs are converted to string sequences using spectral seriation and leading eigenvectors.
    • Graph matching is framed as maximum a posteriori (MAP) sequence alignment.
    • Edit costs are derived from eigenvector components and graph edge densities.

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    Main Results:

    • The proposed method provides a rigorous framework for graph edit distance computation.
    • Sequence alignment probability directly informs edit costs.
    • The novel edit distance is effective for graph clustering tasks.

    Conclusions:

    • Converting graphs to sequences offers a formal approach to graph edit distance.
    • The spectral seriation and MAP alignment method provides a robust way to compare graphs.
    • This technique enhances the utility of graph edit distance in applications like clustering.