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

大数据分析是发现的核心，涵盖了医学信息学、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，并将部署在先进的计算机硬件上。目标是实现对现有数据分析技术的数量级改进，开发对数据中的不完整性、噪声、模糊性和高维具有鲁棒性的算法。特别的重点将是并行和分布式算法，可以有效地解决大问题，并产生准确的解决方案。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。改进后的性能将实现跨应用程序的快速和可扩展的数据分析，从社交网络分析到研究公民对可持续发展相关问题的态度，再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，这两个领域将从交叉受精中取得巨大进步。教育和推广计划包括研究生课程的创建，通过本科生和研究生的研究经历参与代表性不足的群体，以及通过讲习班和小型研讨会组织社区建设工作。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非负矩阵分解（NMF）来执行许多任务，如主题建模、视频数据的背景分离、超光谱成像、网络规模聚类和社区检测。本提案的目标是使用统一的框架开发用于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，并生成一个称为具有非负约束的并行低秩近似（PLANCK）的软件包，该软件包提供高性能，灵活性和可扩展性，以应对当今不断增长的数据集规模。该算法将推广到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。而不是为每个问题域和数学技术开发单独的软件，灵活性将通过在块坐标下降框架的背景下描述几乎所有当前的NMF和NTF算法来实现。使用这个框架可以将共享计算内核（通常会延长运行时间）与特定算法的计算分离开来。最后，所提议的软件的可用性和实用性将通过应用程序驱动、与早期最终用户建立协作以及根据算法和问题增量地概括框架来维持。

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.