Adversarial Attacks on Multi-Network Mining: Problem Definition and Fast Solutions

Multi-sourced networks naturally appear in many application domains, ranging from bioinformatics, social networks, neuroscience to management. Although state-of-the-art offers rich models and algorithms to find various patterns when input networks are given, it has largely remained nascent on how vulnerable the mining results are due to the adversarial attacks. In this paper, we address the problem of attacking multi-network mining through the way of deliberately perturbing the networks to alter the mining results. The key idea of the proposed method (<sc>Admiring</sc>) is effective and efficient influence functions on the Sylvester equation defined over the input networks, which plays a central and unifying role in various multi-network mining tasks. The proposed algorithms bear three main advantages, including (1) <italic>effectiveness,</italic> being able to accurately quantify the rate of change of the mining results in response to attacks; (2) <italic>efficiency,</italic> scaling <italic>linearly</italic> with more than <inline-formula><tex-math notation="LaTeX">$100 \times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>100</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="zhou-ieq1-3078634.gif"/></alternatives></inline-formula> speed-up over the straightforward implementation without any quality loss; and (3) <italic>generality,</italic> being applicable to a variety of multi-network mining tasks (e.g., graph kernel, network alignment, cross-network node similarity) with different attacking strategies (e.g., edge/node removal, attribute alteration).