We address the analysis of sensor networks. We explore new definitions of geometric network connectivity based on manifolds and devise methods for analyzing the connectivity patterns of such networks. In addition, we investigate various norms of diffusion operators as new definitions of correspondence between data sets, establishing nonlinear counterparts of the classical, yet linear cross-correlation.
Such notions of correspondence lead to new (dynamic) connectivity maps between data sets. In the emerging field of signal processing on graphs, connectivity maps assume a central role, where typically prior knowledge is used for their construction. In this context, our capability to extract dynamic connectivity maps from data observations circumvents the need of such prior knowledge and the bias it inherently embodies.