SI2-SSE: Collaborative Research: High Performance Low Rank Approximation for Scalable Data Analytics

大数据分析是发现的核心，涵盖医疗信息学、商业分析、国家安全和材料科学等广泛领域。该项目旨在对一些关键的数据分析问题进行建模，并设计、验证和部署可扩展的知识提取方法。开发的算法将能够处理极端大小的数据集，并可部署在先进的计算机硬件上。其目标是实现对现有数据分析技术的数量级改进，开发对数据的不完整性、噪声、模糊性和高维具有健壮性的算法。特别关注的将是能够有效解决大型问题并产生准确解决方案的并行和分布式算法。拟议的研究和软件开发将使领域专家能够处理需要大型并行系统的大数据集。改进的性能将实现跨应用程序的快速和可扩展的数据分析，从研究公民对可持续发展相关问题的态度的社交网络分析，到优化客户购物体验的计算营销技术。拟议的工作将有助于弥合计算科学和数据分析生态系统之间的差距，这两个领域有望通过交叉受精取得巨大进展。教育和推广计划包括创建研究生课程，通过本科生和研究生的研究经验让未被充分代表的群体参与进来，以及研讨会和小型研讨会组织的社区建设努力。随着互联网规模数据的出现，数据挖掘和机器学习社区采用了非负矩阵分解(NMF)来执行大量任务，如主题建模、背景与视频数据分离、高光谱成像、网络规模聚类和社区检测。该方案的目标是开发使用统一框架计算非负矩阵和张量分解(NMF和NTF)及其变体的高效并行算法，并产生一个称为带非负约束的并行低阶近似(Planck)的软件包，该软件包提供高性能、灵活性和可伸缩性，以应对当今不断增长的数据集。算法将被推广到NTF问题，并扩展了我们可以有效并行化的算法类别；我们的软件框架将允许最终用户使用和扩展我们的技术。不是为每个问题领域和数学技术开发单独的软件，而是通过在块坐标下降框架的背景下表征几乎所有当前的NMF和NTF算法来实现灵活性。使用此框架可以将共享计算内核从特定于算法的计算中分离出来，这通常会延长运行时间。最后，将通过应用程序驱动、与早期终端用户建立协作以及在算法和问题方面逐步推广框架来保持拟议软件的可用性和实用性。

Big Data analytics is at the core of discovery covering vast areas such as medical informatics, business analytics, national security, and materials sciences. This project aims to model some of the key data analytics problems and design, verify, and deploy scalable methods for knowledge extraction. The algorithms developed will be able to handle data sets of extreme sizes and will be deployable on advanced computer hardware. The goal is to realize orders-of-magnitude improvements over existing data analytics technologies, developing algorithms that are robust to incompleteness, noise, ambiguity, and high dimension in the data. Particular focus will be parallel and distributed algorithms that can efficiently solve large problems and produce accurate solutions. The proposed research and software development will allow domain experts to tackle Big Data sets requiring large parallel systems. The improved performance will enable fast and scalable data analysis across applications, from social network analysis to study citizens' attitudes toward sustainability-related issues to computational marketing techniques that refine customers' shopping experiences. The proposed work will help bridge the gap between computational science and data analytics ecosystems, two fields that stand to make great advancements from cross-fertilization. The education and outreach plan includes graduate course creation, engagement of under-represented groups via both undergraduate and graduate research experiences, and community-building efforts by workshop and mini-symposium organization.With the advent of internet-scale data, the data mining and machine learning community has adopted Nonnegative Matrix Factorization (NMF) for performing numerous tasks such as topic modeling, background separation from video data, hyper-spectral imaging, web-scale clustering, and community detection. The goals of this proposal are to develop efficient parallel algorithms for computing nonnegative matrix and tensor factorizations (NMF and NTF) and their variants using a unified framework, and to produce a software package called Parallel Low-rank Approximation with Nonnegative Constraints (PLANCK) that delivers the high performance, flexibility, and scalability necessary to tackle the ever-growing size of today's data sets. The algorithms will be generalized to NTF problems and extend the class of algorithms we can efficiently parallelize; our software framework will allow end-users to use and extend our techniques. Rather than developing separate software for each problem domain and mathematical technique, flexibility will be achieved by characterizing nearly all of the current NMF and NTF algorithms in the context of a block coordinate descent framework. Using this framework the shared computational kernels can be separated, which usually extend run times, from the algorithm-specific computations. Finally, the usability and practicality of the proposed software will be maintained by being application driven, establishing collaborations with early end-users, and by incrementally generalizing the framework in terms of both algorithms and problems.