MRMine: Multi-resolution multi-network embedding

Network embedding has become the cornerstone of a variety of mining tasks, such as classification, link prediction, clustering, anomaly detection and many more, thanks to its superior ability to encode the intrinsic network characteristics in a compact low-dimensional space. Most of the existing methods focus on a single network and/or a single resolution, which generate embeddings of different network objects (node/subgraph/network) from different networks separately. A fundamental limitation with such methods is that the intrinsic relationship across different networks (e.g., two networks share same or similar subgraphs) and that across different resolutions (e.g., the node-subgraph membership) are ignored, resulting in disparate embeddings. Consequentially, it leads to sub-optimal performance or even becomes inapplicable for some downstream mining tasks (e.g., role classification, network alignment. etc.). In this paper, we propose a unified framework (MrMine) to learn the representations of objects from multiple networks at three complementary resolutions (i.e., network, subgraph and node) simultaneously. The key idea is to construct the cross-resolution cross-network context for each object. The proposed method bears two distinctive features. First, it enables and/or boosts various multi-network downstream mining tasks by having embeddings at different resolutions from different networks in the same embedding space. Second, Our method is efficient and scalable, with a O(nloд(n)) time complexity for the base algorithm and a linear time complexity w.r.t. the number of nodes and edges of input networks for the accelerated version. Extensive experiments on real-world data show that our methods (1) are able to enable and enhance a variety of multi-network mining tasks, and (2) scale up to million-node networks.