Spectral Methods: Algorithms and Applications
谱方法:算法和应用
基本信息
- 批准号:0634904
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-10-01 至 2010-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Abstract--------Problems in many areas where the input data is a matrix have been tackled by Spectral Methods which use low-rank approximations to the input matrix. In the important application area of Clustering, only known proofs that the methods succeed have to make the unrealistic assumption that all entries of the matrix arestatistically independent. This research removes this important impediment to the wider use of the method by developing the theory and algorithms that work under limited independence, a much more realistic assumption. To illustrate, in one example - document-term matrices - this research assumes only that thedocuments are statistically independent, not the terms in each document.The research also generalize the methods developed for limited independence to deal with matrix-valued random variables which are of interest in several areas and to date have no substantial work on them. The PI and supported students will extend the applications of spectral-like methods to tensors - multi-dimensional arrays. It is expected that the research here will be one of the key bridges between theory and practice in thisarea, thus leading to a broad transfer of theoretical developments into practice in time.
摘要-输入数据是矩阵的许多领域中的问题已经通过对输入矩阵使用低阶近似的频谱方法来解决。在聚类的重要应用领域,只有已知的方法成功的证明必须假设矩阵的所有项都是统计独立的,这是不现实的。这项研究通过开发在有限独立性下工作的理论和算法,消除了该方法更广泛使用的这一重要障碍,这是一个更现实的假设。为了说明这一点,在一个例子--文档-术语矩阵--中,本研究只假设文档在统计上是独立的,而不是每个文档中的术语。研究还推广了为有限独立性而开发的方法,以处理几个领域中感兴趣的矩阵值随机变量,并且到目前为止还没有对它们进行实质性的研究。PI和被支持的学生将把类谱方法的应用扩展到张量-多维阵列。预计这方面的研究将成为这一领域理论与实践之间的重要桥梁之一,从而使理论发展及时广泛地转化为实践。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Daniel Spielman其他文献
35. Efficacy of Ketamine in Unmedicated Adults With OCD: A Randomized Controlled Trial
- DOI:
10.1016/j.biopsych.2023.02.218 - 发表时间:
2023-05-01 - 期刊:
- 影响因子:
- 作者:
Carolyn Rodriguez;Chi-Ming Chen;Gary Glover;Booil Jo;Daniel Spielman;Leanne Williams;Peter van Roessel;Charles DeBattista;Max Wintermark;Anthony Lombardi;Anthony Pinto;Keara Valentine;Maria Filippou-Frye;Jessica Hawkins;Elizabeth McCarthy;Pavithra Mukunda;Andrea Varias;Jordan Wilson;Brianna Wright - 通讯作者:
Brianna Wright
1.10 THALAMIC METABOLITE LEVELS AND SENSORY PROCESSING IN TWINS WITH AUTISM SPECTRUM DISORDER
- DOI:
10.1016/j.jaac.2016.09.011 - 发表时间:
2016-10-01 - 期刊:
- 影响因子:
- 作者:
John P. Hegarty;Meng Gu;Daniel Spielman;Sue Cleveland;Joachim J. Hallmayer;Laura C. Lazzeroni;Mira Raman;Julio Monterrey;Thomas Frazier;Jennifer M. Phillips;Allan L. Reiss;Antonio Hardan - 通讯作者:
Antonio Hardan
The power of adaptiveness and additional queries in random-self-reductions
- DOI:
10.1007/bf01202287 - 发表时间:
1994-06-01 - 期刊:
- 影响因子:1.000
- 作者:
Joan Feigenbaum;Lance Fortnow;Carsten Lund;Daniel Spielman - 通讯作者:
Daniel Spielman
310. Simultaneous [18F]Flumazenil-Positron Emission Tomography and GABA-Magnetic Resonance Spectroscopy in Adults with Autism and Healthy Volunteers
- DOI:
10.1016/j.biopsych.2017.02.325 - 发表时间:
2017-05-15 - 期刊:
- 影响因子:
- 作者:
Lawrence Fung;Ryan Flores;Meng Gu;Trine Hjoernevik;Antonio Hardan;Daniel Spielman;Frederick Chin - 通讯作者:
Frederick Chin
508 - Proton specfroscopy reveals normal naa concentration in cortical gray mastter in schizophrenic patients
- DOI:
10.1016/s0920-9964(97)82516-9 - 发表时间:
1997-01-01 - 期刊:
- 影响因子:
- 作者:
Kelvin O. Lim;Elfar Adalsteinsson;Daniel Spielman;Edith V. Sullivan;Adolf Pfefferbaum - 通讯作者:
Adolf Pfefferbaum
Daniel Spielman的其他文献
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{{ truncateString('Daniel Spielman', 18)}}的其他基金
AF: Medium: Generalized Algebraic Graph Theory: Algorithms and Analysis
AF:中:广义代数图论:算法与分析
- 批准号:
1562041 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Continuing Grant
AF: Large: Collaborative Research: Algebraic Graph Algorithms: The Laplacian and Beyond
AF:大型:协作研究:代数图算法:拉普拉斯算子及其他算法
- 批准号:
1111257 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Standard Grant
AF: Small: Spectral Graph Theory, Point Clouds, and Linear Equation Solvers
AF:小:谱图理论、点云和线性方程求解器
- 批准号:
0915487 - 财政年份:2009
- 资助金额:
-- - 项目类别:
Standard Grant
Collaborative Research: Spectral Graph Theory and Its Applications
合作研究:谱图理论及其应用
- 批准号:
0634957 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Continuing Grant
ITR: Collaborative Research: Smoothed Analysis of Algorithms
ITR:协作研究:算法的平滑分析
- 批准号:
0707522 - 财政年份:2006
- 资助金额:
-- - 项目类别:
Continuing Grant
ITR: Collaborative Research: Smoothed Analysis of Algorithms
ITR:协作研究:算法的平滑分析
- 批准号:
0324914 - 财政年份:2003
- 资助金额:
-- - 项目类别:
Continuing Grant
ITR/SY(CISE): Why algorithms work well in practice: pertubation-based average-case analysis of the simplex algorithm and beyond
ITR/SY(CISE):为什么算法在实践中表现良好:单纯形算法及其他算法的基于扰动的平均情况分析
- 批准号:
0112487 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Standard Grant
CAREER: Computationally Efficient Error-Correcting Codes and Their Applications
职业:计算高效的纠错码及其应用
- 批准号:
9701304 - 财政年份:1997
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Mathematical Sciences Postdoctoral Research Fellowships
数学科学博士后研究奖学金
- 批准号:
9508950 - 财政年份:1995
- 资助金额:
-- - 项目类别:
Fellowship Award
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