Collaborative Research: Integrating Algebraic Topology, Graph Theory, and Multiscale Analysis for Learning Complex and Diverse Datasets

协作研究：集成代数拓扑、图论和多尺度分析来学习复杂多样的数据集

• 批准号: 2053284
• 负责人: Duc Nguyen
• 金额: $ 15万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2053284&HistoricalAwards=false
• 关键词: Collaborative; Research; Integrating; Algebraic; Topology

Despite the tremendous accomplishments of machine learning and deep learning in the past decade, challenges remain for structurally complex and diverse data. For example, a single data point in a database used for drug design might have tens of thousands of internal degrees of freedom, and such a database may have tens of thousands of such data points. This feature of structural complexity is a major challenge to deep learning methods. Moreover, diverse data typically originate from sparse sampling of a huge space, and this sparsity is due, in particular, to the cost and time constraints in experimental data acquisition. This project will address the challenges of complex and diverse datasets with ideas that blend and integrate mathematical techniques from several subfields including algebraic topology, spectral graph theory and multiscale analysis. The methods developed will apply to data representation, advanced machine learning methods, and deep learning algorithms, and will be implemented into software packages available to the community. This project will train graduate and undergraduate students and engage underrepresented groups in data science research. This project will develop novel topology and graph theory-based approaches to revolutionize the current practice in data analysis and to deal with the challenge of structurally complex data and diverse data. First, the investigators will develop persistent combinatorial graph theory as a unified paradigm for simultaneous topological data analysis and spectral data analysis. In particular, they will develop systematic, scalable, accurate persistent combinatorial graph representations to extract rich topological and spectral information. Secondly, the investigators will develop multiscale graph models to create a family of nested submanifolds to handle the diverse data originated from sparsely sampled data points in a huge space. These methods will be integrated with advanced machine learning and deep learning algorithms for complex and diverse datasets. Thirdly, the proposed methods will be applied to a wide range of case studies in data science. User-friendly software packages and online servers will be developed using parallel and GPU architectures for researchers who are not formally trained in mathematics or machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

尽管在过去十年中，机器学习和深度学习取得了巨大成就，但对于结构复杂和多样化的数据仍然存在挑战。例如，用于药物设计的数据库中的单个数据点可能具有数万个内部自由度，并且这样的数据库可能具有数以万计的此类数据点。结构复杂性的这一特征是深度学习方法的主要挑战。 此外，多样的数据通常源于巨大空间的稀疏采样，这种稀疏性尤其是由于实验数据获取的成本和时间限制。 该项目将通过融合和整合来自几个子领域的数学技术（包括代数拓扑，光谱图理论和多尺度分析）的数学技术的想法来应对复杂和多样化的数据集的挑战。所开发的方法将适用于数据表示，高级机器学习方法和深度学习算法，并将实施到社区可用的软件包中。该项目将培训毕业生和本科生，并参与代表性不足的小组参与数据科学研究。该项目将开发新颖的拓扑和基于图理论的方法，以彻底改变数据分析中当前的实践，并应对结构复杂的数据和多样化数据的挑战。首先，研究人员将开发持久的组合图理论，作为同时拓扑数据分析和光谱数据分析的统一范式。 特别是，它们将开发系统的，可扩展的，准确的持续组合图表示，以提取丰富的拓扑和光谱信息。其次，调查人员将开发多尺度图模型，以创建一个嵌套的子手机系列，以处理源自巨大空间中稀疏采样的数据点的不同数据。这些方法将与高级机器学习和复杂和多样化数据集的深度学习算法集成。 第三，提出的方法将应用于数据科学的广泛案例研究。用户友好的软件包和在线服务器将使用平行和GPU架构开发针对未接受数学或机器学习正式培训的研究人员。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来通过评估来获得支持的。

项目成果

Novel Molecular Representations Using Neumann-Cayley Orthogonal Gated Recurrent Unit

• DOI: 10.1021/acs.jcim.2c01526
• 发表时间: 2023-04
• 期刊: Journal of chemical information and modeling
• 影响因子: 5.6
• 作者: Edison Mucllari;Vasily Zadorozhnyy;Qiang Ye;D. Nguyen

Geometric graph learning with extended atom-types features for protein-ligand binding affinity prediction

• DOI: 10.1016/j.compbiomed.2023.107250
• 发表时间: 2023-07-27
• 期刊: COMPUTERS IN BIOLOGY AND MEDICINE
• 影响因子: 7.7
• 作者: Rana，Md Masud;Nguyen，Duc Duy
• 通讯作者: Nguyen，Duc Duy

Multiscale laplacian learning

• DOI: 10.1007/s10489-022-04333-2
• 发表时间: 2021-09
• 期刊: Applied Intelligence
• 影响因子: 5.3
• 作者: E. Merkurjev;D. Nguyen;Guo-Wei Wei-Guo-Wei-Wei-2113827098