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Outlier detection, or the identification of observations that differ significantly from the norm, is an important aspect of data mining. Conventional outlier detection tools have limited applicability to networks, in which there are interdependencies between the variables. In this paper, we consider the problem of identifying unusual spatial distributions of nodal signals on a graph. Leveraging tools from graph signal processing and statistical analysis, we propose a methodology to identify outliers in graph signals in a computationally efficient manner. Specifically, we examine a projection of the graph signal into a lower dimensional representation that enables easier outlier identification. Additionally, we derive analytical expressions for the outlier bounds. We apply our technique by identifying off-nominal days in the context of the US airport network using aviation delay data.

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Understanding the characteristics of air-traffic delays and disruptions is critical for developing ways to mitigate their significant economic and environmental impacts. Conventional delay-performance metrics reflect only the magnitude of incurred flightdelays at airports; in this work, we show that it is also important to characterize the spatial distribution of delays across a network of airports. We analyze graph-supported signals, leveraging techniques from spectral theory and graph-signal processing to compute analytical and simulation-driven bounds for identifying outliers in spatial distribution. We then apply these methods to the case of airport-delay networks and demonstrate the applicability of our methods by analyzing U.S. airport delays from 2008 through 2017. We also perform an airline-specific analysis, deriving insights into the delay dynamics of individual airline subnetworks. Through our analysis, we highlight key differences in delay dynamics between different types of disruptions, ranging from nor’easters and hurricanes to airport outages. We also examine delay interactions between airline subnetworks and the system-wide network and compile an inventory of outlier days that could guide future aviation operations and research. In doing so, we demonstrate how our approach can provide operational insights in an air-transportation setting. Our analysis provides a complementary metric to conventional aviation-delay benchmarks and aids airlines, traffic-flow managers, and transportation-system planners in quantifying offnominal system performance.

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