Modelling and Mining Complex Networks

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Currently, we experience a rapid growth of research done in the intersection of mining and modelling of social networks. This research proposal concentrates on problems from this intersection. There are two main reasons to include random graph models in mining complex networks: - - Synthetic models. Many important algorithms (such as community detection algorithms) are unsupervised in nature. Moreover, despite the fact that the research community gets better with exchanging datasets (see, for example, Stanford Large Network Dataset Collection) there are still very few publicly available networks with known underlying structure, the so-called ground truth. Hence, to test, benchmark, and properly tune unsupervised algorithms, one may use random graphs to produce synthetic "playground": graphs with known ground truth (such as the community structure in the context of community detection algorithms). - - Null -models. Null--model is a random object that matches one specific property P of a given object but is otherwise taken, unbiasedly, at random from the family of objects that have property P. As a result, the null-models can be used to test whether a given object exhibits some "surprising" property that is not expected on the basis of chance alone or as an implication of the fact that the object has property P. It is expected that both applications of random graphs will continue to gain their importance. My experience with industrial projects allows me to identify missing tools and algorithms that are of interest to the practitioners. On the other hand, my pure research background allows me to better understand processes that shape self-organizing complex networks and, as a result, to be better prepared to design efficient algorithms that work on data collected from real-world applications. In the proposal, we will discuss in detail the following objectives: - Unsupervised Framework for Evaluating of Node Embedding Algorithms, - Community Detection in Networks Modelled as Hypergraphs, - Generating Synthetic Networks. In each of these sub-projects, rigorous definitions, theorems, and proofs (that will be published in research papers) are needed to design the tool, and the tool will be implemented in Julia language (that will be made publicly available on GitHub repository) and carefully tested on both synthetic and real- world networks.