Modelling and Mining Complex Networks

目前，我们经历了社会网络挖掘和建模交叉领域研究的快速增长。本研究计划集中于这一交叉点的问题。在复杂网络挖掘中使用随机图模型主要有两个原因：——合成模型。许多重要的算法（如社区检测算法）本质上是无监督的。此外，尽管研究社区在交换数据集方面做得越来越好（例如，参见斯坦福大学大型网络数据集集），但仍然很少有公开可用的网络具有已知的底层结构，即所谓的基础真相。因此，为了测试、基准测试和适当调优无监督算法，可以使用随机图来生成合成的“游乐场”：具有已知基本真理的图（例如社区检测算法上下文中的社区结构）。- -空模型。零,模型是一个随机的对象匹配一个给定对象的特定特性P,但否则,无偏,随机从对象的家庭财产P .因此,null-models可以用来测试是否一个给定对象的展览一些“令人惊讶的”属性的基础上预计不会机会单独或作为一个隐含的事实对象属性P .预计随机图形的两个应用程序将继续获得它们的重要性。我在工业项目中的经验使我能够识别从业者感兴趣的缺失工具和算法。另一方面，我纯粹的研究背景使我能够更好地理解塑造自组织复杂网络的过程，从而更好地准备设计有效的算法，处理从现实世界中收集的数据。在提案中，我们将详细讨论以下目标：-评估节点嵌入算法的无监督框架，-超图建模网络中的社区检测，-生成合成网络。在每个子项目中，需要严格的定义、定理和证明（将在研究论文中发表）来设计工具，并且该工具将用Julia语言实现（将在GitHub存储库上公开可用），并在合成和现实世界的网络上仔细测试。

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.