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PATHATTACK: attacking shortest paths in complex networks

Summary

Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide Web. An adversary with the capability to perturb the graph might make the shortest path between two nodes route traffic through advantageous portions of the graph (e.g., a toll road he owns). In this paper, we introduce the Force Path Cut problem, in which there is a specific route the adversary wants to promote by removing a minimum number of edges in the graph. We show that Force Path Cut is NP-complete, but also that it can be recast as an instance of the Weighted Set Cover problem, enabling the use of approximation algorithms. The size of the universe for the set cover problem is potentially factorial in the number of nodes. To overcome this hurdle, we propose the PATHATTACK algorithm, which via constraint generation considers only a small subset of paths|at most 5% of the number of edges in 99% of our experiments. Across a diverse set of synthetic and real networks, the linear programming formulation of Weighted Set Cover yields the optimal solution in over 98% of cases. We also demonstrate a time/cost tradeoff using two approximation algorithms and greedy baseline methods. This work provides a foundation for addressing similar problems and expands the area of adversarial graph mining beyond recent work on node classification and embedding.
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Summary

Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide Web. An adversary with the capability to perturb the graph might make the shortest path...

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Attacking Embeddings to Counter Community Detection

Published in:
Network Science Society Conference 2020 [submitted]

Summary

Community detection can be an extremely useful data triage tool, enabling a data analyst to split a largenetwork into smaller portions for a deeper analysis. If, however, a particular node wanted to avoid scrutiny, it could strategically create new connections that make it seem uninteresting. In this work, we investigate theuse of a state-of-the-art attack against node embedding as a means of countering community detection whilebeing blind to the attributes of others. The attack proposed in [1] attempts to maximize the loss function beingminimized by a random-walk-based embedding method (where two nodes are made closer together the more often a random walk starting at one node ends at the other). We propose using this method to attack thecommunity structure of the graph, specifically attacking the community assignment of an adversarial vertex. Since nodes in the same community tend to appear near each other in a random walk, their continuous-space embedding also tend to be close. Thus, we aim to use the general embedding attack in an attempt to shift the community membership of the adversarial vertex. To test this strategy, we adopt an experimental framework as in [2], where each node is given a “temperature” indicating how interesting it is. A node’s temperature can be “hot,” “cold,” or “unknown.” A node can perturbitself by adding new edges to any other node in the graph. The node’s goal is to be placed in a community thatis cold, i.e., where the average node temperature is less than 0. Of the 5 attacks proposed in [2], we use 2 in our experiments. The simpler attack is Cold and Lonely, which first connects to cold nodes, then unknown, then hot, and connects within each temperature in order of increasing degree. The more sophisticated attack is StableStructure. The procedure for this attack is to (1) identify stable structures (containing nodes assigned to the same community each time for several trials), (2) connect to nodes in order of increasing average temperature of their stable structures (randomly within a structure), and (3) connect to nodes with no stable structure in order of increasing temperature. As in [2], we use the Louvain modularity maximization technique for community detection. We slightly modify the embedding attack of [1] by only allowing addition of new edges and requiring that they include the adversary vertex. Since the embedding attack is blind to the temperatures of the nodes, experimenting with these attacks gives insight into how much this attribute information helps the adversary. Experimental results are shown in Figure 1. Graphs considered in these experiments are (1) an 500-node Erdos-Renyi graph with edge probabilityp= 0.02, (2) a stochastic block model with 5 communities of 100nodes each and edge probabilities ofpin= 0.06 andpout= 0.01, (3) the network of Abu Sayyaf Group (ASG)—aviolent non-state Islamist group operating in the Philippines—where two nodes are linked if they both participatein at least one kidnapping event, with labels derived from stable structures (nodes together in at least 95% of 1000 Louvain trials), and (4) the Cora machine learning citation graph, with 7 classes based on subjectarea. Temperature is assigned to the Erdos-Renyi nodes randomly with probability 0.25, 0.5, and 0.25 for hot,unknown, and cold, respectively. For the other graphs, nodes with the same label as the target are hot, unknown,and cold with probability 0.35, 0.55, and 0.1, respectively, and the hot and cold probabilities are swapped forother labels. The results demonstrate that, even without the temperature information, the embedding methodis about as effective as the Cold and Lonely when there is community structure to exploit, though it is not aseffective as Stable Structure, which leverages both community structure and temperature information.
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Summary

Community detection can be an extremely useful data triage tool, enabling a data analyst to split a largenetwork into smaller portions for a deeper analysis. If, however, a particular node wanted to avoid scrutiny, it could strategically create new connections that make it seem uninteresting. In this work, we investigate...

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Complex Network Effects on the Robustness of Graph Convolutional Networks

Summary

Vertex classification—the problem of identifying the class labels of nodes in a graph—has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation net-works or roles of machines in a computer network. Recent work has demonstrated that vertex classification using graph convolutional networks is susceptible to targeted poisoning attacks, in which both graph structure and node attributes can be changed in anattempt to misclassify a target node. This vulnerability decreases users’ confidence in the learning method and can prevent adoption in high-stakes contexts. This paper presents the first work aimed at leveraging network characteristics to improve robustness of these methods. Our focus is on using network features to choose the training set, rather than selecting the training set at random. Our alternative methods of selecting training data are (1) to select the highest-degree nodes in each class and (2) to iteratively select the node with the most neighbors minimally connected to the training set. In the datasets on which the original attack was demonstrated, we show that changing the training set can make the network much harder to attack. To maintain a given probability of attack success, the adversary must use far more perturbations; often a factor of 2–4 over the random training baseline. This increase in robustness is often as substantial as tripling the amount of randomly selected training data. Even in cases where success is relatively easy for the attacker, we show that classification performance degrades much more gradually using the proposed methods, with weaker incorrect predictions for the attacked nodes. Finally, we investigate the potential tradeoff between robustness and performance in various datasets.
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Summary

Vertex classification—the problem of identifying the class labels of nodes in a graph—has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation net-works or roles of machines in a computer network. Recent work has demonstrated that vertex classification using graph convolutional networks is...

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Topological effects on attacks against vertex classification

Summary

Vertex classification is vulnerable to perturbations of both graph topology and vertex attributes, as shown in recent research. As in other machine learning domains, concerns about robustness to adversarial manipulation can prevent potential users from adopting proposed methods when the consequence of action is very high. This paper considers two topological characteristics of graphs and explores the way these features affect the amount the adversary must perturb the graph in order to be successful. We show that, if certain vertices are included in the training set, it is possible to substantially an adversary's required perturbation budget. On four citation datasets, we demonstrate that if the training set includes high degree vertices or vertices that ensure all unlabeled nodes have neighbors in the training set, we show that the adversary's budget often increases by a substantial factor---often a factor of 2 or more---over random training for the Nettack poisoning attack. Even for especially easy targets (those that are misclassified after just one or two perturbations), the degradation of performance is much slower, assigning much lower probabilities to the incorrect classes. In addition, we demonstrate that this robustness either persists when recently proposed defenses are applied, or is competitive with the resulting performance improvement for the defender.
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Summary

Vertex classification is vulnerable to perturbations of both graph topology and vertex attributes, as shown in recent research. As in other machine learning domains, concerns about robustness to adversarial manipulation can prevent potential users from adopting proposed methods when the consequence of action is very high. This paper considers two...

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Improving robustness to attacks against vertex classification

Published in:
15th Intl. Workshop on Mining and Learning with Graphs, 5 August 2019.

Summary

Vertex classification—the problem of identifying the class labels of nodes in a graph—has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation networks or roles of machines in a computer network. Recent work has demonstrated that vertex classification using graph convolutional networks is susceptible to targeted poisoning attacks, in which both graph structure and node attributes can be changed in an attempt to misclassify a target node. This vulnerability decreases users' confidence in the learning method and can prevent adoption in high-stakes contexts. This paper presents work in progress aiming to make vertex classification robust to these types of attacks. We investigate two aspects of this problem: (1) the classification model and (2) the method for selecting training data. Our alternative classifier is a support vector machine (with a radial basis function kernel), which is applied to an augmented node feature-vector obtained by appending the node’s attributes to a Euclidean vector representing the node based on the graph structure. Our alternative methods of selecting training data are (1) to select the highest-degree nodes in each class and (2) to iteratively select the node with the most neighbors minimally connected to the training set. In the datasets on which the original attack was demonstrated, we show that changing the training set can make the network much harder to attack. To maintain a given probability of attack success, the adversary must use far more perturbations; often a factor of 2–4 over the random training baseline. Even in cases where success is relatively easy for the attacker, we show that the classification and training alternatives allow classification performance to degrade much more gradually, with weaker incorrect predictions for the attacked nodes.
READ LESS

Summary

Vertex classification—the problem of identifying the class labels of nodes in a graph—has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation networks or roles of machines in a computer network. Recent work has demonstrated that vertex classification using graph convolutional networks is...

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