MSPA-MCS: Collaborative Research: Fast Nonnegative Matrix Factorizations: Theory, Algorithms, and Applications

MSPA-MCS:协作研究:快速非负矩阵分解:理论、算法和应用

基本信息

  • 批准号:
    0732299
  • 负责人:
  • 金额:
    $ 23万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2007
  • 资助国家:
    美国
  • 起止时间:
    2007-10-01 至 2011-09-30
  • 项目状态:
    已结题

项目摘要

Proposal ID(s): 0732318 and 0732299PI(s): Haesun Park and Moody ChuInstitition(s): GaTech and NCSUTitle: Collaborative Research: Fast Nonnegative Matrix Factorizations: Theory, Algorithms, and ApplicationsABSTRACT:Mathematical models with nonnegative data values are abounding in sciences and engineering. For the sake of physical feasibility and interpretability, the nature of nonnegative must be retained in computation and analysis. This work concerns itself with the factorization of nonnegative matrix into product of lower rank nonnegative matrices. Such a notion of the nonnegative matrix factorization plays a major role in a wide range of important applications including text mining, cheminformatics, factor retrieval, image articulation, bioinformatics, and in dimension reduction and clustering in pattern and data analysis. The discoveries from this proposed research are expected to impact not only the advanced theoretical foundations of matrix computation, but also contribute to the general areas of data mining such as dimension reduction, clustering, and visualization.The basic question behind the nonnegative matrix factorization (NMF) is to best approximate a given nonnegative data matrix as the product of two lower dimensional and, hence, lower rank nonnegative matrices. The two lower rank matrices provides lot of essential information that, otherwise, would be difficult to retrieve from the original matrix. Many NMF techniques have been proposed in the literature, yet there is still little theory on how the NMF can be robustly and efficiently solved. In this work, development of new faster algorithms will be conducted through structured and comprehensive performance evaluation of promising research directions, including the active set and geometry based algorithms, against real-world application data to obtain valuable insights. The proposed study of the geometric structure of the NMF and theoretical properties of the NMF algorithms, such as convergence, should provide the basis of assessment for any NMF methods. Applicability of the NMF to dimension reduction and clustering will also be investigated. Results of this research are also likely to have potential applications in database management, medical examination and diagnosis, bio-chemical selection, and biological networks.
提案ID(S):0732318和0732299PI(S):Haesun Park和Moody ChuinStitition(S):Gatech和NCSUTITLE:协作研究:合作研究:快速的非阴性矩阵因素化:理论,算法,算法和应用程序的模型:非整合数据的值科学和工程。为了身体的可行性和解释性,必须保留在计算和分析中。这项工作涉及非负矩阵分解为较低等级矩阵的乘积。这种非负矩阵分解的概念在广泛的重要应用中起着重要作用,包括文本挖掘,化学信息学,因子检索,图像表达,生物信息学,以及在模式和数据分析中降低维度和聚类中。这项拟议研究的发现不仅会影响矩阵计算的先进理论基础,而且还会影响数据挖掘的一般领域,例如降低,聚类和可视化。 )可以最好地近似给定的非负数据矩阵作为两个较低维的乘积,因此,较低等级的非负矩阵。两个较低的等级矩阵提供了很多基本信息,否则,很难从原始矩阵中检索。文献中已经提出了许多NMF技术,但是关于如何稳健有效地解决NMF仍然几乎没有理论。在这项工作中,将通过对现实世界应用程序数据的有前途的研究方向的结构化和全面的绩效评估(包括主动集和几何算法)来开发新的更快的算法,以获得有价值的见解。对NMF的几何结构的拟议研究和NMF算法的理论特性(例如收敛)应为任何NMF方法提供评估的基础。 NMF对降低和聚类的适用性也将进行研究。这项研究的结果也可能在数据库管理,体检和诊断,生物化学选择和生物网络中具有潜在的应用。

项目成果

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Moody Chu其他文献

Moody Chu的其他文献

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{{ truncateString('Moody Chu', 18)}}的其他基金

Preparing Hamiltonians for Quantum Simulation: A Computational Framework for Cartan Decomposition via Lax Dynamics
为量子模拟准备哈密顿量:通过 Lax 动力学进行嘉当分解的计算框架
  • 批准号:
    2309376
  • 财政年份:
    2023
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
From Quantum Entanglement to Tensor Decomposition by Global Optimization
从量子纠缠到全局优化的张量分解
  • 批准号:
    1912816
  • 财政年份:
    2019
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Numerical Algorithms as Dynamcal Systems - Structure Preservation, Convergence Theory, and Rediscretization
作为动态系统的数值算法 - 结构保持、收敛理论和重新离散化
  • 批准号:
    1316779
  • 财政年份:
    2013
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Automated Structure Generation, Error Correction, and Semi-Definite Programming Techniques for Structured Quadratic Inverse Eigenvale Problems: Theory, Algorithms and Applications
结构化二次反特征值问题的自动结构生成、纠错和半定编程技术:理论、算法和应用
  • 批准号:
    1014666
  • 财政年份:
    2010
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Collaborative Proposal: Quadratic Inverse Eigenvalue Problems for Model Updating in Science and Engineering: Theory and Computation
合作提案:科学与工程模型更新的二次逆特征值问题:理论与计算
  • 批准号:
    0505880
  • 财政年份:
    2005
  • 资助金额:
    $ 23万
  • 项目类别:
    Continuing Grant
The Centroid Decomposition and Other Approximations to the SVD
SVD 的质心分解和其他近似
  • 批准号:
    0204157
  • 财政年份:
    2002
  • 资助金额:
    $ 23万
  • 项目类别:
    Continuing Grant
Algorithms for the Inverse Problem of Matrix Construction
矩阵构造反问题的算法
  • 批准号:
    0073056
  • 财政年份:
    2000
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Adaptive Control Algorithms for Adaptive Optics Applications
用于自适应光学应用的自适应控制算法
  • 批准号:
    9803759
  • 财政年份:
    1998
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Inverse Eigenvalue Problems
数学科学:反特征值问题
  • 批准号:
    9422280
  • 财政年份:
    1995
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Matrix Differential Equations and Their Applications
数学科学:矩阵微分方程及其应用
  • 批准号:
    9123448
  • 财政年份:
    1992
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant

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MSPA-MCS: Collaborative Research: Algorithms for Near-Optimal Multistage Decision-Making under Uncertainty: Online Learning from Historical Samples
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  • 批准号:
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  • 财政年份:
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  • 项目类别:
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  • 资助金额:
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    Standard Grant
MSPA-MCS: Collaborative Research: Fast Nonnegative Matrix Factorizations: Theory, Algorithms, and Applications
MSPA-MCS:协作研究:快速非负矩阵分解:理论、算法和应用
  • 批准号:
    0732318
  • 财政年份:
    2007
  • 资助金额:
    $ 23万
  • 项目类别:
    Standard Grant
MSPA-MCS: Collaborative Research: Algorithms for Near-Optimal Multistage Decision-Making under Uncertainty: Online Learning from Historical Samples
MSPA-MCS:协作研究:不确定性下近乎最优的多阶段决策算法:历史样本在线学习
  • 批准号:
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