Functional Object Data Analysis and its Applications

函数对象数据分析及其应用

基本信息

  • 批准号:
    EP/K021672/1
  • 负责人:
  • 金额:
    $ 106.56万
  • 依托单位:
  • 依托单位国家:
    英国
  • 项目类别:
    Fellowship
  • 财政年份:
    2013
  • 资助国家:
    英国
  • 起止时间:
    2013 至 无数据
  • 项目状态:
    已结题

项目摘要

When linguists are trying to determine how different languages are related or neuroscientists wish to know how one part of the brain is associated with another, how to analyse data which is both complex and massive is a fundamental question. However, an area of Statistics, namely Functional Data Analysis, where the data is described as mathematical functions rather than numbers or vectors, has recently been shown to be very powerful in these situations. This fellowship aims to take functional data analysis and advance it so that much more complex data can be investigated. This will require establishing a careful statistical framework for the analysis of such functions even in situations where the functions have strict relationships. By considering the underlying mathematical spaces which the functions lie in, it is possible to construct valid statistical procedures, which preserve these relationships, such as the functions needing to be positive definite or the functions needing to be related by a graph or network.As an example, comparison between different languages (for example, how is French quantitatively different from Italian) can be carried out in the framework of functional data but not without considering specifically how the data should be analysed to take into account its particular properties. For example in trying to find a path from one language to another, it would be sensible to try to only go via other feasible acoustic sounds. This turns out to be mathematically related to shape analysis, a simple example of which might be how to describe going from London to Sydney. The shortest path is through the centre of the Earth, but this is not sensible, so you have to go round the world. Establishing links between shape analysis and functional data is a major aim of this fellowship. In addition, most brain analysis currently splits the brain up into lots of elements know as voxels, and then analyses these voxels one by one. However, the brain is really one object (or complex 3-D object) which should be analysed together. This is another example of functional data and the methods developed in this fellowship will enable the analysis of the brain as a single object. This will be done by examining the types of dependence between observations in brain imaging data, and using these to build such an object. Of particular interest will be the analysis of brain connections resulting from particular tasks which will require a mixture of functional data analysis and graphical or network analysis. However, before this can be done and the resulting insights into the brain found, the statistical methods required to do this need to be developed.
When linguists are trying to determine how different languages are related or neuroscientists wish to know how one part of the brain is associated with another, how to analyse data which is both complex and massive is a fundamental question. However, an area of Statistics, namely Functional Data Analysis, where the data is described as mathematical functions rather than numbers or vectors, has recently been shown to be very powerful in these situations. This fellowship aims to take functional data analysis and advance it so that much more complex data can be investigated. This will require establishing a careful statistical framework for the analysis of such functions even in situations where the functions have strict relationships. By considering the underlying mathematical spaces which the functions lie in, it is possible to construct valid statistical procedures, which preserve these relationships, such as the functions needing to be positive definite or the functions needing to be related by a graph or network.As an example, comparison between different languages (for example, how is French quantitatively different from Italian) can be carried out in the framework of functional data but not without considering specifically how the data should be analysed to take into account its particular properties. For example in trying to find a path from one language to another, it would be sensible to try to only go via other feasible acoustic sounds. This turns out to be mathematically related to shape analysis, a simple example of which might be how to describe going from London to Sydney. The shortest path is through the centre of the Earth, but this is not sensible, so you have to go round the world. Establishing links between shape analysis and functional data is a major aim of this fellowship. In addition, most brain analysis currently splits the brain up into lots of elements know as voxels, and then analyses these voxels one by one. However, the brain is really one object (or complex 3-D object) which should be analysed together. This is another example of functional data and the methods developed in this fellowship will enable the analysis of the brain as a single object. This will be done by examining the types of dependence between observations in brain imaging data, and using these to build such an object. Of particular interest will be the analysis of brain connections resulting from particular tasks which will require a mixture of functional data analysis and graphical or network analysis. However, before this can be done and the resulting insights into the brain found, the statistical methods required to do this need to be developed.

项目成果

期刊论文数量(10)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A functional approach to deconvolve dynamic neuroimaging data
一种对动态神经影像数据进行反卷积的功能方法
  • DOI:
    10.48550/arxiv.1411.2051
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Jiang C
  • 通讯作者:
    Jiang C
Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese.
Tests for separability in nonparametric covariance operators of random surfaces
  • DOI:
    10.1214/16-aos1495
  • 发表时间:
    2015-05
  • 期刊:
  • 影响因子:
    0
  • 作者:
    J. Aston;D. Pigoli;Shahin Tavakoli
  • 通讯作者:
    J. Aston;D. Pigoli;Shahin Tavakoli
SMOOTH PRINCIPAL COMPONENT ANALYSIS OVER TWO-DIMENSIONAL MANIFOLDS WITH AN APPLICATION TO NEUROIMAGING
  • DOI:
    10.1214/16-aoas975
  • 发表时间:
    2016-12-01
  • 期刊:
  • 影响因子:
    1.8
  • 作者:
    Lila, Eardi;Aston, John A. D.;Sangalli, Laura M.
  • 通讯作者:
    Sangalli, Laura M.
A Functional Approach to Deconvolve Dynamic Neuroimaging Data.
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John Aston其他文献

Screening method for Enzyme-based liquefaction of corn stover pellets at high solids
高固体含量玉米秸秆颗粒酶法液化的筛选方法
  • DOI:
    10.1016/j.biortech.2022.127999
  • 发表时间:
    2022-11-01
  • 期刊:
  • 影响因子:
    9.000
  • 作者:
    Luana Assis Serra;Rosineide Gomes da Silva Cruz;Diana M.R. Gutierrez;Antonio José Gonçalves Cruz;Carlos Alberto Torres Canizares;Xueli Chen;Nathan Mosier;David Thompson;John Aston;James Dooley;Pankaj Sharma;Janice Lisboa De Marco;João Ricardo Moreira de Almeida;Kendra Erk;Eduardo Ximenes;Michael R. Ladisch
  • 通讯作者:
    Michael R. Ladisch

John Aston的其他文献

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{{ truncateString('John Aston', 18)}}的其他基金

Real-time digital optimisation and decision making for energy and transport systems
能源和运输系统的实时数字优化和决策
  • 批准号:
    EP/Y004841/1
  • 财政年份:
    2023
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Research Grant
Functional Object Data Analysis and its Applications
函数对象数据分析及其应用
  • 批准号:
    EP/K021672/2
  • 财政年份:
    2014
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Fellowship
Functional Phylogenies
功能系统发育
  • 批准号:
    EP/H046224/1
  • 财政年份:
    2010
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Research Grant
Statistical Analysis of Non-Linear Spatio-Temporal Signals with particular application to Functional Neuroimaging
非线性时空信号的统计分析,特别适用于功能神经影像
  • 批准号:
    EP/H016856/1
  • 财政年份:
    2010
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Research Grant

相似海外基金

Collaborative Research: Halfspace Depth for Object and Functional Data
协作研究:对象和功能数据的半空间深度
  • 批准号:
    2329879
  • 财政年份:
    2023
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Continuing Grant
Collaborative Research: Halfspace Depth for Object and Functional Data
协作研究:对象和功能数据的半空间深度
  • 批准号:
    2113713
  • 财政年份:
    2021
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    $ 106.56万
  • 项目类别:
    Continuing Grant
Collaborative Research: Halfspace Depth for Object and Functional Data
协作研究:对象和功能数据的半空间深度
  • 批准号:
    2113696
  • 财政年份:
    2021
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Standard Grant
Models for Complex Functional and Object Data
复杂功能和对象数据的模型
  • 批准号:
    2014626
  • 财政年份:
    2020
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Standard Grant
Functional Object Data Analysis and its Applications
函数对象数据分析及其应用
  • 批准号:
    EP/K021672/2
  • 财政年份:
    2014
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Fellowship
Optimization theory and algorithms in functional and object-oriented data analysis: from quantitative to qualitative aspects
函数式和面向对象数据分析中的优化理论和算法:从定量到定性
  • 批准号:
    238598-2010
  • 财政年份:
    2014
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Discovery Grants Program - Individual
Optimization theory and algorithms in functional and object-oriented data analysis: from quantitative to qualitative aspects
函数式和面向对象数据分析中的优化理论和算法:从定量到定性
  • 批准号:
    238598-2010
  • 财政年份:
    2013
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Discovery Grants Program - Individual
Optimization theory and algorithms in functional and object-oriented data analysis: from quantitative to qualitative aspects
函数式和面向对象数据分析中的优化理论和算法:从定量到定性
  • 批准号:
    396103-2010
  • 财政年份:
    2012
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Discovery Grants Program - Accelerator Supplements
Optimization theory and algorithms in functional and object-oriented data analysis: from quantitative to qualitative aspects
函数式和面向对象数据分析中的优化理论和算法:从定量到定性
  • 批准号:
    238598-2010
  • 财政年份:
    2012
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Discovery Grants Program - Individual
Optimization theory and algorithms in functional and object-oriented data analysis: from quantitative to qualitative aspects
函数式和面向对象数据分析中的优化理论和算法:从定量到定性
  • 批准号:
    396103-2010
  • 财政年份:
    2011
  • 资助金额:
    $ 106.56万
  • 项目类别:
    Discovery Grants Program - Accelerator Supplements
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