We describe a new transform that generates a dictionary of bases
for handling data on a graph by combining recursive partitioning of the graph
and the Laplacian eigenvectors of each subgraph. Similar to the wavelet
packet and local cosine dictionaries for regularly sampled signals,
this dictionary of bases on the graph allows one to select an orthonormal
basis that is most suitable to one's task at hand using a best-basis type
algorithm. We also describe a few related transforms including a version
of the Haar wavelet transform on a graph, each of which may be useful in
its own right.
Keywords:
Graph Laplacian eigenvectors, Fiedler vectors, spectral graph partitioning, a dictionary of orthonormal bases, wavelet-like transforms on graphs