Multilevel Algorithms for Tensor and Network Problems

这一建议为基于张量的数据处理、马尔可夫链建模和社会网络分析领域中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)，需要新的可扩展的算法方法，并且它们在我们快速发展的基于知识的经济中具有巨大的经济潜力。这项拟议的研究将利用申请者研究小组最近进行的开创性工作。基于张量的数据处理在数据挖掘、推荐系统和网络安全中正迅速变得越来越重要；表征电信系统(例如呼叫中心)的复杂排队网络的现实马尔可夫链模型由于模型的高维而具有挑战性；高级社交网络分析为社交网络公司带来重要的竞争优势。将为那些具有挑战性的新出现的问题类开发新的数值算法。 拟议的研究结果有望对加拿大大有裨益：对大数据集计算密集型问题的算法探索是我们快速发展的信息经济的关键组成部分。该提案中开发的数值算法将直接应用于加拿大的经济和社会，用于社交网络分析、科学计算中的大数据、多模式张量数据处理、呼叫中心建模和网络安全。此外，拟议的工作将培训具有关键算法和大规模分布式计算技能的高素质人员，这些技能对加拿大的知识经济至关重要。

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. The results of the proposed research promise to be of great benefit to Canada: algorithmic exploration of compute-intensive problems with large data sets is a crucial building block in our rapidly evolving information economy. The numerical algorithms developed in this proposal will have direct applications in Canada's economy and society, for social networking analysis, big data in scientific computing, multi-modal tensor data processing, call centre modeling, and cybersecurity. Moreover, the proposed work will train highly qualified personnel with critical algorithmic and large-scale distributed computing skills that are essential for Canada's knowledge economy.