Multiscale `Spatial' Analysis of Network Data: Putting Wavelets on Graphs.
Eric D. Kolaczyk, (Boston University), firstname.lastname@example.org
Massive amounts of data currently are being gathered in a variety of contexts in which the underlying structure is that of a network. This includes measurements of intra- and internet traffic, but also data from sensor networks, social networks, etc. Often, though not always, there is a well-defined spatial context corresponding to the network, such as that induced by router or sensor locations. However, strict interpretation of the data within this context can be misleading, and viewing the measurements from the context of a graph topology typically is more appropriate. Nevertheless, just as in traditional spatial analysis, the concept of `scale' can play an important role in the analysis of network data, such as in problems centered on the detection of anomalies or the determination of the concentration/diffuseness of an attack. I will present an overview of ongoing work with colleagues on the development of tools for the analysis of graph-indexed data at multiple scales. A common theme throughout will be on extensions of the wavelet paradigm to arbitrary graphs, as well as descriptive and inferential tools for analysis under the resulting alternative data representation. Illustrations will be provided using internet traffic data.