Identifying shortest paths between nodes in a network is an important task in many applications. Recent work has shown that a malicious actor can manipulate a graph to make traffic between two nodes of interest follow their target path. In this paper, we develop a defense against such attacks by modifying the edge weights that users observe. The defender must balance inhibiting the attacker against any negative effects on benign users. Specifically, the defender’s goals are: (a) recommend the shortest paths to users, (b) make the lengths of the shortest paths in the published graph close to those of the same paths in the true graph, and (c) minimize the probability of an attack. We formulate the defense as a Stackelberg game in which the defender is the leader and the attacker is the follower. We also consider a zero-sum version of the game in which the defender’s goal is to minimize cost while achieving the minimum possible attack probability. We show that the defense problem is NP-hard and propose heuristic solutions for both the zero-sum and non-zero-sum settings. By relaxing some constraints of the original problem, we formulate a linear program for local optimization around a feasible point. We present defense results with both synthetic and real networks and show that our methods often reach the lower bound of the defender’s cost.

Abstract In this work, we explore multiplex graph (networks with different types of edges) generation with deep generative models. We discuss some of the challenges associated with multiplex graph generation that make it a more difficult problem than traditional graph generation. We propose TenGAN, the first neural network for multiplex graph generation, which greatly reduces the number of parameters required for multiplex graph generation. We also propose 3 different criteria for evaluating the quality of generated graphs: a graph-attribute-based, a classifier-based, and a tensor-based method. We evaluate its performance on 4 datasets and show that it generally performs better than other existing statistical multiplex graph generative models. We also adapt HGEN, an existing deep generative model for heterogeneous information networks, to work for multiplex graphs and show that our method generally performs better.

Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic patterns to gain some benefit (e.g., make more money by directing traffic to a toll road). This article presents theForce Path Cutproblem, in which an adversary removes edges from a graph to make a particular path the shortest between its terminal nodes. We prove that the optimization version of this problem is APX-hard but introducePATHATTACK, a polynomial-time approximation algorithm that guarantees a solution within a logarithmic factor of the optimal value. In addition, we introduce theForce Edge CutandForce Node Cutproblems, in which the adversary targets a particular edge or node, respectively, rather than an entire path. We derive a nonconvex optimization formulation for these problems and derive a heuristic algorithm that usesPATHATTACKas a subroutine. We demonstrate all of these algorithms on a diverse set of real and synthetic networks, illustrating where the proposed algorithms provide the greatest improvement over baseline methods.

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 where PCA-based detection methods fail. In this paper, we demonstrate that applying sparse PCA to low-rank approximations of the modularity matrix is a viable solution to the planted clique problem that enables detection of small planted cliques in graphs where running the standard semidefinite program for sparse PCA is not possible.

Recent work on signal detection in graph-based data focuses on classical detection when the signal and noise are both in the form of discrete entities and their relationships. In practice, the relationships of interest may not be directly observable, or may be observed through a noisy mechanism. The effects of imperfect observations add another layer of difficulty to the detection problem, beyond the effects of typical random fluctuations in the background graph. This paper analyzes the impact on detection performance of several error and corruption mechanisms for graph data. In relatively simple scenarios, the change in signal and noise power is analyzed, and this is demonstrated empirically in more complicated models. It is shown that, with enough side information, it is possible to fully recover performance equivalent to working with uncorrupted data using a Bayesian approach, and a simpler cost-optimization approach is shown to provide a substantial benefit as well.

Nonlinear effects limit analog circuit performance, causing both in-band and out-of-band distortion. The classical Volterra series provides an accurate model of many nonlinear systems, but the number of parameters grows extremely quickly as the memory depth and polynomial order are increased. Recently, concepts from compressed sensing have been applied to nonlinear system modeling in order to address this issue. This work investigates the theory and practice of applying compressed sensing techniques to nonlinear system identification under the constraints of typical radio frequency (RF) laboratories. The main theoretical result shows that these techniques are capable of identifying sparse Memory Polynomials using only single-tone training signals rather than pseudorandom noise. Empirical results using laboratory measurements of an RF receiver show that sparse Generalized Memory Polynomials can also be recovered from two-tone signals.

When working with large-scale network data, the interconnected entities often have additional descriptive information. This additional metadata may provide insight that can be exploited for detection of anomalous events. In this paper, we use a generalized linear model for random attributed graphs to model connection probabilities using vertex metadata. For a class of such models, we show that an approximation to the exact model yields an exploitable structure in the edge probabilities, allowing for efficient scaling of a spectral framework for anomaly detection through analysis of graph residuals, and a fast and simple procedure for estimating the model parameters. In simulation, we demonstrate that taking into account both attributes and dynamics in this analysis has a much more significant impact on the detection of an emerging anomaly than accounting for either dynamics or attributes alone. We also present an analysis of a large, dynamic citation graph, demonstrating that taking additional document metadata into account emphasizes parts of the graph that would not be considered significant otherwise.

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

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 analysis and subgraph detection. The data are stored in a new format that allows easy extraction of graphs representing any relationship existing in the data. The principal analysis algorithm is the partial eigendecomposition of the modularity matrix, whose running time is discussed. A large document dataset is analyzed, and we present subgraphs that stand out in the principal eigenspace of the time-varying graphs, including behavior we regard as clutter as well as small, tightly-connected clusters that emerge over time.

Anomaly detection in graphs is a relevant problem in numerous applications. When determining whether an observation is anomalous with respect to the model of typical behavior, the notion of “goodness of fit” is important. This notion, however, is not well-understood in the context of graph data. In this paper, we propose three goodness-of-fit statistics for Chung-Lu random graphs, and analyze their efficacy in discriminating graphs generated by the Chung-Lu model from those with anomalous topologies. In the results of a Monte Carlo simulation, we see that the most powerful statistic for anomaly detection depends on the type of anomaly, suggesting that a hybrid statistic would be the most powerful.

This letter proposes a new model for preferential attachment in dynamic directed networks. This model consists of a linear time-invariant system that uses past observations to predict future attachment rates, and an innovation noise process that induces growth on vertices that previously had no attachments. Analyzing a large citation network in this context, we show that the proposed model fits the data better than existing preferential attachment models. An analysis of the noise in the dataset reveals power-law degree distributions often seen in large networks, and polynomial decay with respect to age in the probability of citing yet-uncited documents.

Efficient operation of RF power amplifiers requires compensation strategies to mitigate nonlinear behavior. As band-width increases, memory effects become more pronounced, and Volterra series based compensation becomes onerous due to the exponential growth in the number of necessary coefficients. Behavioral models such as Wiener-Hammerstein systems with a parallel feedforward or feedback filter are more tractable but more difficult to identify. In this paper, we extend a Wiener-Hammerstein identification method to such systems showing that identification is possible (up to inherent model ambiguities) from single- and two-tone measurements. We also calculate the Cramer-Rao bound for the system parameters and compare to our identification method in simulation. Finally, we demonstrate equalization performance using measured data from a wideband GaN power amplifier.

Graphs are canonical examples of high-dimensional non-Euclidean data sets, and are emerging as a common data structure in many fields. While there are many algorithms to analyze such data, a signal processing theory for evaluating these techniques akin to detection and estimation in the classical Euclidean setting remains to be developed. In this paper we show the conceptual advantages gained by formulating graph analysis problems in a signal processing framework by way of a practical example: detection of a subgraph embedded in a background graph. We describe an approach based on detection theory and provide empirical results indicating that the test statistic proposed has reasonable power to detect dense subgraphs in large random graphs.

When working with network datasets, the theoretical framework of detection theory for Euclidean vector spaces no longer applies. Nevertheless, it is desirable to determine the detectability of small, anomalous graphs embedded into background networks with known statistical properties. Casting the problem of subgraph detection in a signal processing context, this article provides a framework and empirical results that elucidate a detection theory" for graph-valued data. Its focus is the detection of anomalies in unweighted, undirected graphs through L1 properties of the eigenvectors of the graph’s so-called modularity matrix. This metric is observed to have relatively low variance for certain categories of randomly-generated graphs, and to reveal the presence of an anomalous subgraph with reasonable reliability when the anomaly is not well-correlated with stronger portions of the background graph. An analysis of subgraphs in real network datasets confirms the efficacy of this approach."

In this paper we present a simple closed-form solution to the Wiener-Hammerstein (W-H) identification problem. The identification process occurs in the log-frequency domain where magnitudes and phases are separable. We show that the theoretically optimal W-H identification is unique up to an amplitude, phase and delay ambiguity, and that the nonlinearity enables the separate identification of the individual linear time invariant (LTI) components in a W-H architecture.

Certain types of non-Gaussian noise sources in multicarrier communication systems behave effectively as modulating signals that control the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian and non-Gaussian noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. Impulsive interferers and timing-phase error are examples of such non-Gaussian noise sources. The BER-equivalent power of a composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the amplified version of the underlying Gaussian noise source. The amplification factor is derived from the characteristics of the non-Gaussian noise source. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.

Impulse noise in multicarrier communication systems behaves effectively as a modulating signal that controls the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian noise and impulse noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. The BER-equivalent power of the composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the amplified version of the underlying Gaussian noise source. The amplification factor is derived from the characteristics of the impulse interference. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.