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Planted cluster detection is an important form of signal detection when the data are in the form of a graph. When there are multiple graphs representing multiple connection types, the method of aggregation can have significant impact on the results of a detection algorithm. This paper addresses the tradeoff between two possible aggregation methods: convex combination and intersection. For a spectral...
A common problem in network analysis is detecting small subgraphs of interest within a large background graph. This includes multi-source fusion scenarios where data from several modalities must be integrated to form the network. This paper presents an application of novel techniques leveraging the signal processing for graphs algorithmic framework, to well-studied collaboration networks in the field...
Detection of clusters and communities in graphs is useful in a wide range of applications. In this paper we investigate the problem of detecting a clique embedded in a random graph. Recent results have demonstrated a sharp detectability threshold for a simple algorithm based on principal component analysis (PCA). Sparse PCA of the graph's modularity matrix can successfully discover clique locations...
This paper outlines techniques for optimization of filter coefficients in a spectral framework for anomalous subgraph detection. Restricting the scope to the detection of a known signal in i.i.d. noise, the optimal coefficients for maximizing the signal's power are shown to be found via a rank-1 tensor approximation of the subgraph's dynamic topology. While this technique optimizes our power metric,...
In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the entire processing chain, from data storage to graph construction to graph...
We present a simple model for self-pulsation instability in passively phased high power optical fiber amplifier arrays with external feedback. Its key features are, first, the feedback level's sensitivity, and thus that of the cavity Q-value, to small phase changes of the array fields, and, second, the effect of refractive index nonlinearity in the amplifiers. The model's prediction of an instability...
The problem of detecting a small, anomalous subgraph within a large background network is important and applicable to many fields. The non-Euclidean nature of graph data, however, complicates the application of classical detection theory in this context. A recent statistical framework for anomalous subgraph detection uses spectral properties of a graph's modularity matrix to determine the presence...
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