Levenshtein distance for graph spectral features

Graph structures play a critical role in computer vision, but they are inconvenient to use in pattern recognition tasks because of their combinatorial nature and the consequent difficulty in constructing feature vectors. Spectral representations have been used for this task which are based on the eigensystem of the graph Laplacian matrix. However, graphs of different sizes produce eigensystems of different sizes where not all eigenmodes are present in both graphs. We use the Levenshtein distance to compare spectral representations under graph edit operations which add or delete vertices. The spectral representations are therefore of different sizes. We use the concept of the string-edit distance to allow for the missing eigenmodes and compare the correct modes to each other. We evaluate the method by first using generated graphs to compare the effect of vertex deletion operations. We then examine the performance of the method on graphs from a shape database.