Dimension Reduction and Complex High-Dimensional Data

降维和复杂的高维数据

基本信息

  • 批准号:
    RGPIN-2021-04073
  • 负责人:
  • 金额:
    $ 1.31万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2021
  • 资助国家:
    加拿大
  • 起止时间:
    2021-01-01 至 2022-12-31
  • 项目状态:
    已结题

项目摘要

Recent technological advances in many fields of science have led to the routine collection of vast amounts of data. The collected data is typically high--dimensional and highly correlated. My research interests lie in adapting and extending dimension reduction methods to accommodate the complexities of these high--throughput biological data. As part of my research program, the challenges that my students and I will tackle over the next five years can be grouped into three objectives. First, missing data is common in any applied science, but it is particularly problematic with high--throughput data. Moreover, the nature of multivariate data implies that complete--case analysis can discard a significant amount of information. To increase efficiency, I will look at how multiple imputation procedures can be used with multivariate methods. To this end, I will describe the distribution of aggregates of test statistics common in multivariate analysis, and I will reformulate the optimisation problem of these methods to accommodate missing data. Second, building on some of my previous work, I will incorporate a priori knowledge through correlation structures. For example, the linear correlation patterns observed in DNA methylation data can be accounted for in dimension reduction methods by using autoregressive covariance structures. I will then look at extending this work to incorporate spatial correlation, which is common in neuroimaging data. I will also study hierarchical probabilistic multivariate models in order to model correlation between observations. Third, complex correlation also manifests through the complex geometry of the sample space, such as with image and text data. Topological data analysis provides tools to study the geometric structure of our data. I will develop simulation frameworks to study the impact of this geometry on multivariate methods. I will use this knowledge to develop methods to generate synthetic data to oversample imbalanced data. I will also combine tools from multivariate analysis and topological data analysis to extend PCEV, CCA and PLS to nonlinear dimension reduction methods. The research program proposed here will have an impact across multiple disciplines. All proposed methodologies will be implemented in software packages, so that applied researchers can more easily use them in their work and methodological researchers can more rapidly build upon them.
许多科学领域的最新技术进步导致了大量数据的常规收集。所收集的数据通常是高维和高度相关的。我的研究兴趣在于调整和扩展降维方法,以适应这些高通量生物数据的复杂性。作为我的研究计划的一部分,我和我的学生在未来五年内将面临的挑战可以分为三个目标。首先,数据缺失在任何应用科学中都是常见的,但它在高通量数据中尤其成问题。此外,多变量数据的性质意味着完整的案例分析可以丢弃大量的信息。为了提高效率,我将研究如何将多重插补程序与多变量方法一起使用。为此,我将描述多元分析中常见的检验统计量的聚集分布,并重新制定这些方法的优化问题,以适应缺失数据。第二,在我以前的一些工作的基础上,我将通过相关性结构结合先验知识。例如,在DNA甲基化数据中观察到的线性相关模式可以通过使用自回归协方差结构在降维方法中解释。然后,我将研究扩展这项工作,以纳入空间相关性,这在神经成像数据中很常见。我还将研究层次概率多变量模型,以模拟观测之间的相关性。第三,复杂的相关性也通过样本空间的复杂几何形状来体现,例如图像和文本数据。拓扑数据分析提供了研究数据几何结构的工具。我将开发模拟框架来研究这种几何结构对多元方法的影响。我将使用这些知识来开发方法来生成合成数据,以过采样不平衡数据。我也将结合联合收割机工具,从多元分析和拓扑数据分析,扩展PCEV,CCA和PLS的非线性降维方法。这里提出的研究计划将对多个学科产生影响。所有拟议的方法将在软件包中实施,以便应用研究人员可以更容易地在工作中使用它们,方法研究人员可以更快地建立在它们的基础上。

项目成果

期刊论文数量(0)
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科研奖励数量(0)
会议论文数量(0)
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Turgeon, Maxime其他文献

Principal component of explained variance: An efficient and optimal data dimension reduction framework for association studies
  • DOI:
    10.1177/0962280216660128
  • 发表时间:
    2018-05-01
  • 期刊:
  • 影响因子:
    2.3
  • 作者:
    Turgeon, Maxime;Oualkacha, Karim;Labbe, Aurelie
  • 通讯作者:
    Labbe, Aurelie
A Mendelian randomization study of the effect of type-2 diabetes on coronary heart disease.
  • DOI:
    10.1038/ncomms8060
  • 发表时间:
    2015-05-28
  • 期刊:
  • 影响因子:
    16.6
  • 作者:
    Ahmad, Omar S.;Morris, John A.;Mujammami, Muhammad;Forgetta, Vincenzo;Leong, Aaron;Li, Rui;Turgeon, Maxime;Greenwood, Celia M. T.;Thanassoulis, George;Meigs, James B.;Sladek, Robert;Richards, J. Brent
  • 通讯作者:
    Richards, J. Brent

Turgeon, Maxime的其他文献

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{{ truncateString('Turgeon, Maxime', 18)}}的其他基金

Dimension Reduction and Complex High-Dimensional Data
降维和复杂的高维数据
  • 批准号:
    RGPIN-2021-04073
  • 财政年份:
    2022
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Grants Program - Individual
Dimension Reduction and Complex High-Dimensional Data
降维和复杂的高维数据
  • 批准号:
    DGECR-2021-00296
  • 财政年份:
    2021
  • 资助金额:
    $ 1.31万
  • 项目类别:
    Discovery Launch Supplement

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