The independent and principal component of graph spectra

In this paper, we demonstrate how PCA and ICA can be used for embedding graphs in pattern-spaces. Graph spectral feature vectors are calculated from the leading eigenvalues and eigenvectors of the unweighted graph adjacency matrix. The vectors are then embedded in a lower dimensional pattern space using both the PCA and ICA decomposition methods. Synthetic and real sequences are tested using the proposed graph clustering algorithm. The preliminary results show that generally speaking the ICA is better than PCA for clustering graphs. The best choice of graph spectral feature for clustering is the cluster shared perimeters.