Robustly Identifying Dependent Components in Multiple High-Dimensional Data Sets Based on Few Observations

基于少量观察稳健地识别多个高维数据集中的相关组件

• 批准号: 262301625
• 负责人: Professor Peter Schreier, Ph.D.
• 金额: --
• 依托单位: Fachgebiet Signalverarbeitung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/262301625?language=en
• 关键词: Robustly; Identifying; Dependent; Components; Multiple

The objective of this proposal is the development of methods to robustly identify dependent components in multiple high-dimensional data structures, where sample support is relatively small. Many algorithms require this information as an input parameter. For instance, in biomedicine, there are established approaches for fusing the data from different brain imaging modalities, but in order to apply them, we need to know the dependent components in different feature sets. As another example, in sensor array processing, many algorithms for resolving sources (e.g. estimating their direction of arrival) need to have prior information about the number of sources impinging upon the array. Often, this problem is solved ad hoc, with greatly varying results. The development of systematic approaches will therefore be of interest to a wide array of areas in the natural sciences and engineering. The focus of our proposal will be on the theory, but in order to illustrate and investigate the performance of our methods, we will choose some selected applications in biomedicine. More specifically, in this proposal, our objectives are: - To develop model-selection rules for multiple data sets with relatively small sample support. Treating multiple data sets is much more difficult than finding dependencies between two data sets because there are many possible dependence structures. The very few existing approaches work only for large sample support and make very restrictive assumptions about the underlying correlation structure.- To make our second-order techniques robust against deviations from Gaussianity. This is critical in order to be able to deal with heavy-tailed noise and outliers, which are commonplace in many applications. - To first build a theory based on second-order correlations, which consider linear dependencies between data sets, and then extend our approaches to also take into account nonlinear dependencies. - To investigate the restrictions that small sample support imposes on the identifiability of nonlinear dependencies. Obviously, we would expect that the number of samples determines the amount of information that can be extracted from the data sets. - To apply our techniques to some selected problems in biomedicine. It is expected that these applications will benefit greatly from this research project. It is still commonplace in the biomedical community to solve model-selection problems using ad-hoc approaches and rules of thumb. A systematic approach will help provide more convincing and satisfying solutions.

本提案的目标是开发方法来健壮地识别多个高维数据结构中的相关组件，其中样本支持相对较小。许多算法需要这些信息作为输入参数。例如，在生物医学中，已经建立了融合不同脑成像模式数据的方法，但为了应用它们，我们需要知道不同特征集中的依赖成分。另一个例子是，在传感器阵列处理中，许多用于解析源的算法（例如估计它们的到达方向）需要有关于撞击阵列的源数量的先验信息。通常，这个问题是临时解决的，结果差别很大。因此，系统方法的发展将引起自然科学和工程领域广泛领域的兴趣。我们的建议的重点将是理论，但为了说明和调查我们的方法的性能，我们将选择一些在生物医学中的应用。更具体地说，在本提案中，我们的目标是：-开发具有相对较小样本支持的多个数据集的模型选择规则。处理多个数据集比查找两个数据集之间的依赖关系要困难得多，因为存在许多可能的依赖结构。很少有现有的方法只适用于大样本支持，并且对潜在的相关结构做出了非常严格的假设。-使我们的二阶技术对高斯偏差具有鲁棒性。为了能够处理在许多应用中常见的重尾噪声和异常值，这一点至关重要。-首先建立一个基于二阶相关性的理论，考虑数据集之间的线性依赖关系，然后扩展我们的方法，也考虑到非线性依赖关系。-研究小样本支持对非线性依赖关系可识别性的限制。显然，我们期望样本的数量决定了可以从数据集中提取的信息量。-将我们的技术应用于生物医学的一些选定问题。预计这些应用将大大受益于本研究项目。在生物医学界，使用特别的方法和经验法则来解决模型选择问题仍然是司空见惯的。系统的方法将有助于提供更有说服力和令人满意的解决方案。