How to identify global trends from local decisions? Event region detection on mobile networks

Abstract

Abstract-The decentralized detection of event regions is a fundamental building block for monitoring and reasoning about spatial phenomena. However, so far the problem has been studied almost exclusively for static networks. This study proposes a theoretical framework with which we can analyze event detection algorithms suitable for large-scale mobile networks. Our analysis builds on the following insight: the inherent trends of spatial events are well captured by the spectral domain of the network graph. Using this framework, we propose novel local algorithms that are location-free; that work with mobile nodes and dynamic events; that operate on 3D topologies; and that are simple to implement. We are not aware of event detection algorithms possessing all these traits. Simulations based on complex oil spill traces showcase the resilience and robustness of our methods. Additionally, we demonstrate their validity for practical scenarios by evaluating them on a 105 node testbed.

Filtering Random Graph Processes Over Random Time-Varying Graphs

“…In [12], we introduced ARMA graph filters as a special class of IIR graph filters. Differently from the other IIR graph filters [11], [25], ARMA filters capture naturally time-variations of the graph topology and graph signal, and have well-understood behavior for deterministic timevariations [13] showing larger robustness than FIR filters. The most practical implementation (due to its improved stability) of an ARMA filter of order K (ARMA K ) can be obtained by using a parallel bank of K ARMA 1 filters.…”

Graph scale-space theory for distributed peak and pit identification

“…For instance, the deep structure could be used to extend current topological methods for signal mapping and compression to multiple scales [22,29], thus making distributed pattern recognition possible. A second potential application is event-region detection [18]. Tracking event-boundaries across scale has the potential to improve the resilience of current algorithms to phantom effects.…”

“…The third approach is slightly more complex: instead of computing a graph kernel using power iteration (as in (2)), we will use an alternative recursion that -converges-linearly to the output without being affected by asynchrony. Though such recursions have been shown to hold great promise for graph kernels in general [18,19], Theorem 2 shows that they cannot be used in our case: The intuition of the proof is that, whereas (Ksx)(u) is truncated, i.e., it takes into account -at most-the values in an s-hop neighborhood of u, any kernel computed by the third approach decays asymptotically with the number of hops. Therefore, no 1-st order recursion converges exactly to Ks.…”

“…Intuitively, this means that peaks lying on sparse subgraphs and containing many bottleneck links are attenuated first. For a more in-depth characterization of the influence of the graph spectrum, the reader is directed to the relevant literature on graph filters [18,23].…”

“…Based on the scale parameter, a low-pass graph filter controls the size of observable signal structures, attenuating structures of small size, such as noise [28]. Graph filters are also useful for revealing communities [25], identifying event-regions (band-pass) [18], and detecting anomalies (high-pass) [21].…”