EAGER: Fast and Accurate Nonnegative Tensor Decompositions: Algorithms and Software

EAGER：快速准确的非负张量分解：算法和软件

• 批准号: 0956517
• 负责人: Haesun Park
• 金额: $ 11.69万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0956517&HistoricalAwards=false
• 关键词: EAGER; Fast; Accurate; Nonnegative; Tensor

EAGER: Fast and Accurate Nonnegative Tensor Decompositions: Algorithms and Software During the past decades, numerous efficient and effective data analysis algorithms have been designed where data sets are represented as two dimensional arrays, i.e., matrices. However, matrix based methods have limitations since modern data sets are multi-scale and multi-dimensional. In numerous applications, data sets are more naturally represented as tensors than matrices including image analysis, climate modeling, chemometrics, genome signal analysis, and biometric recognition. In this project, the mathematical characteristics of tensor decompositions will be studied. Algorithms will be designed for large scale data analysis that can reveal complex relationships among many dimensions which matrix based methods often cannot. Computations on tensors are expected to extend many of the advantages that the matrix based data analysis methods have offered. Tensor-based methods can be utilized for data compression, modeling, regression, and fusing of information obtained from different sources and scales. Tensor based methods are relatively new in many application areas and theoretical and algorithmic developments, especially for large scale problems, have been slow even in the areas where they have been heavily utilized. The key goals of the project include extension of the matrix decomposition techniques such as the SVD to higher order tensors and develop efficient algorithms for large scale analysis of multi-dimensional data and design their higher-order extensions, development of algorithms for the computation of various nonnegative matrix factorizations (NMF) and nonnegative tensor factorizations (NTF) and study of the mathematical properties of the algorithms, such as robustness, efficiency and accuracy, and implement them in publicly available software. This research will substantially improve the possibility of detailed study of larger scale multi dimensional data sets in numerous application areas including text mining, biological network analysis, and medical examination and diagnosis.

EAGER：快速准确的非负张量分解：算法和软件在过去的几十年中，人们设计了许多高效且有效的数据分析算法，其中数据集表示为二维数组（即矩阵）。 然而，由于现代数据集是多尺度和多维的，基于矩阵的方法具有局限性。在许多应用中，数据集比矩阵更自然地表示为张量，包括图像分析、气候建模、化学计量学、基因组信号分析和生物识别。在这个项目中，将研究张量分解的数学特性。算法将被设计用于大规模数据分析，可以揭示许多维度之间的复杂关系，而基于矩阵的方法通常无法揭示这些关系。张量计算有望扩展基于矩阵的数据分析方法所提供的许多优点。 基于张量的方法可用于数据压缩、建模、回归和融合从不同来源和规模获得的信息。基于张量的方法在许多应用领域相对较新，即使在它们被大量使用的领域，理论和算法的发展（特别是对于大规模问题）也很缓慢。 该项目的主要目标包括将矩阵分解技术（例如 SVD）扩展到高阶张量，开发用于大规模多维数据分析的有效算法并设计其高阶扩展，开发计算各种非负矩阵分解（NMF）和非负张量分解（NTF）的算法以及研究 算法，例如鲁棒性、效率和准确性，并在公开可用的软件中实现它们。这项研究将极大地提高在文本挖掘、生物网络分析以及医学检查和诊断等众多应用领域中对更大规模多维数据集进行详细研究的可能性。