Attacking Embeddings to Counter Community Detection
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.