Multiple Network Embedding for Anomaly Detection in Time Series of Graphs

Abstract

This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of temporally anomalous vertices. We approach these tasks via the adaptation of statistically principled methods for joint graph inference, specifically multiple adjacency spectral embedding (MASE) and omnibus embedding (OMNI). We demonstrate that these two methods are effective for our inference tasks. Moreover, we assess the performance of these methods in terms of the underlying nature of detectable anomalies. Our results delineate the relative strengths and limitations of these procedures, and provide insight into their use. Applied to a large-scale commercial search engine time series of graphs, our approaches demonstrate their applicability and identify the anomalous vertices beyond just large degree change.

Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labels

“…A great amount of inference in the RDPG setting is predicated upon X being a suitably accurate estimate of X, and the key statistical properties of consistency and asymptotic residual normality are established for the ASE in [51,39,48] and [5,4] respectively. These results (and analogues for unscaled variants of the ASE) have laid the groundwork for myriad subsequent inference results, including clustering [51,39,33,49], classification [54], time-series analysis [10,45], and vertex nomination [19,60], among others. In the shuffled testing analysis that we consider herein, we will use the following ASE consistency result from [48,16].…”

“…We finally present these estimated powers averaged over the outer nM C 1 = 50 Monte Carlo replicates. Results are displayed in Figures 5-6 where we range k = (10,20,30,50,75,100) and different k values are represented by different colors/shapes of the plotted lines. Here ≤ k, the number shuffled in the alternative (i.e., the number of actual incorrect labels in U k,n ) ranges over the values plotted on the x-axis.…”

ATOM: AI-Powered Sustainable Resource Management for Serverless Edge Computing Environments

“…Recurrent Deterministic Policy Gradient (RDPG): It works as an extension of Deterministic Policy Gradient (DPG) and is a robust algorithm in scenarios such as time series forecasting [31]. RDPG and DDPG algorithms differ from each other in handling time series patterns.…”