Semi-supervised blockmodelling with pairwise guidance

![CDATA[Blockmodelling is an important technique for detecting underlying patterns in graphs. Existing blockmodelling algorithms are unsupervised and cannot take advantage of the existing information that might be available about objects that are known to be similar. This background information can help finding complex patterns, such as hierarchical or ring blockmodel structures, which are difficult for traditional blockmodelling algorithms to detect. In this paper, we propose a new semi-supervised framework for blockmodelling, which allows background information to be incorporated in the form of pairwise membership information. Our proposed framework is based on the use of Lagrange multipliers and can be incorporated into existing iterative blockmodelling algorithms, enabling them to find complex blockmodel patterns in graphs. We demonstrate the utility of our framework for discovering complex patterns, via experiments over a range of synthetic and real data sets. Code related to this paper is available at: https://people.eng.unimelb.edu.au/mganji/.]]