The Graph Analysis Toolbox: Image Processing on Arbitrary Graphs

Office of Naval Research (N00014-01-1-0624)

Graph Wavelets for Spatial Traffic Analysis

A number of problems in network operations and engineering call for new methods of traffic analysis. While most existing traffic analysis methods are fundamentally temporal, there is a clear need for the analysis of traffic across multiple network links — that is, for spatial traffic analysis. In this paper we give examples of problems that can be addressed via spatial traffic analysis. We then propose a formal approach to spatial traffic analysis based on the wavelet transform. Our approach (graph wavelets) generalizes the traditional wavelet transform so that it can be applied to data elements connected via an arbitrary graph topology. We explore the necessary and desirable properties of this approach and consider some of its possible realizations. We then apply graph wavelets to measurements from an operating network. Our results show that graph wavelets are very useful for our motivating problems; for example, they can be used to form highly summarized views of an entire network's traffic load, to gain insight into a network's global traffic response to a link failure, and to localize the extent of a failure event within the network.