Multilevel Algorithms for Tensor and Network Problems

本提案为基于张量的数据处理、马尔可夫链建模和社会网络分析等领域出现的新型大规模科学计算问题开发了新的算法和软件。这些问题的共同点是数据集可能非常大（“大数据”），需要新的可扩展算法方法，并且在我们快速发展的知识经济中具有巨大的经济潜力。拟议的研究将利用申请人研究小组最近取得的突破性成果。基于张量的数据处理在数据挖掘、推荐系统和网络安全中的重要性正在迅速增加；电信系统（如呼叫中心）特征的复杂排队网络的现实马尔可夫链模型由于模型的高维性而具有挑战性；先进的社交网络分析为社交网络公司带来了重要的竞争优势。新的数值算法将为那些具有挑战性的新兴问题类开发。

This proposal develops novel algorithms and software for new classes of large-scale scientific computing problems that are emerging in the areas of tensor-based data processing, Markov chain modeling, and social network analysis. These problems have in common that data sets may be very large ('Big Data'), that new scalable algorithmic approaches are required, and that they have tremendous economical potential in our fast-evolving knowledge-based economy. The proposed research will capitalize on groundbreaking work that was produced recently in the applicant's research group. Tensor-based data processing is rapidly gaining importance in data mining, recommendation systems, and cybersecurity; realistic Markov chain models of complex queueing networks that characterize telecommunications systems (e.g., call centres) are challenging due to the high dimensionality of the models; and advanced social network analysis leads to important competitive advantages for social network companies. New numerical algorithms will be developed for those challenging emerging problem classes.