Graph Spectral Decomposition and Clustering

This paper investigates the spectral description methods for unweighted graph sequences and the clustering of spectral features in feature spaces. First, the corner features in 2D images of 3D polyhedral objects are represented as neighborhood graphs. Adjacency matrices are constructed from Delaunay graphs of the corners. Then the eigenmodes are defined by the leading eigenvectors of the adjacency matrices. For each eigenmode, we compute the vectors of spectral properties, which include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode adjacency matrix and inter-mode edge distance. Then these vectors are embedded into a pattern space by multidimensional scaling on the L2 norm for pairs of pattern vectors. Meanwhile, the performances of different embedding methods are compared. Finally, the clustering results by k-means method are shown