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A theory and algorithm for detecting and classifying weak, distributed patterns in network data is presented. The patterns we consider are anomalous temporal correlations between signals recorded at sensor nodes in a network. We use robust matrix completion and second order analysis to detect distributed patterns that are not discernible at the level of individual sensors. When viewed independently, the data at each node cannot provide a definitive determination of the underlying pattern, but when fused with data from across the network the relevant patterns emerge. We are specifically interested in detecting weak patterns in computer networks where the nodes (terminals, routers, servers, etc.) are sensors that provide measurements (of packet rates, user activity, central processing unit usage, etc.). The approach is applicable to many other types of sensor networks including wireless networks, mobile sensor networks, and social networks where correlated phenomena are of interest.