#### Active Network Alignment: A Matching-Based Approach

##### Eric Malmi, Aristides Gionis, Evimaria Terzi

Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications-from biological networks to social networks to ontologies-where multiple networked data sources need to be integrated. Due to the difficulty of the task, an accurate alignment can rarely be found without human assistance. Thus, it is of great practical importance to develop network alignment algorithms that can optimally leverage experts who are able to provide the correct alignment for a small number of nodes. Yet, only a handful of existing works address this active network alignment setting. The majority of the existing active methods focus on absolute queries ("are nodes $a$ and $b$ the same or not?"), whereas we argue that it is generally easier for a human expert to answer relative queries ("which node in the set $\{b_1, \ldots, b_n\}$ is the most similar to node $a$?"). This paper introduces two novel relative-query strategies, TopMatchings and GibbsMatchings, which can be applied on top of any network alignment method that constructs and solves a bipartite matching problem. Our methods identify the most informative nodes to query by sampling the matchings of the bipartite graph associated to the network-alignment instance. We compare the proposed approaches to several commonly-used query strategies and perform experiments on both synthetic and real-world datasets. Our sampling-based strategies yield the highest overall performance, outperforming all the baseline methods by more than 15 percentage points in some cases. In terms of accuracy, TopMatchings and GibbsMatchings perform comparably. However, GibbsMatchings is significantly more scalable, but it also requires hyperparameter tuning for a temperature parameter.

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