Invariant Coordinate Selection (ICS): A Robust Statistical Perspective on Independent Component Analysis (ICA)

不变坐标选择 (ICS)：独立成分分析 (ICA) 的稳健统计视角

• 批准号: 0604596
• 负责人: David Tyler
• 金额: $ 13.8万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604596&HistoricalAwards=false
• 关键词: Invariant; Coordinate; Selection; ICS; Robust

ABSTRACTIndependent component analysis (ICA) is an increasingly popular method for analyzing multivariate data within many diverse disciplines, such as computer vision, psychology, electrical engineering, physics and meteorology. Although essentially a multivariate statistical method, the primary development of ICAhas come from outside the area of statistics. Methods developed for ICA presume somewhat specialized models for multivariate data. Nevertheless, these methods tend to possess some natural robustness properties, and consequently, have been used for exploratory data analysis in general and for cluster analysis or unsupervised learning in particular. At present, the statistical properties of ICA methods are not well understood. One goal of the proposed research is thus to conduct a study of the statistical and robustness properties of ICA methods. Another goal of the proposed research is to study the use of ICA methods as general multivariate statistical methods rather than simply as solutions to the ICA problem. To accomplish this, a new model free interpretation of ICA methods, together with some extensions of these methods, is to be introduced and developed. The principal investigator refers to this model free approach as invariant coordinate selection (ICS).The proposed research should have an impact on the many scientific and engineering disciples using ICA models by providing a better statistical understanding of their methods, consequently leading to improved methods and applications. An important application of ICA models, for example, is in the unraveling of convoluted signals or sources. The proposed research will also help call further attention to these important statistical problems to the general statistics research community. In addition, it is anticipated that the proposed introduction and development of the ICS methodology will provide important and potentially very popular new methods for exploring and analyzing multivariate data, perhaps similar to the importance of principal component analysis or discriminant analysis. These more general ICS methods should have impact not only within the statistics community but also within the varied disciplines, such as psychology, biology, geology, and others, that routinely deal with multivariate data.

摘要独立成分分析 (ICA) 是一种越来越流行的方法，用于分析计算机视觉、心理学、电气工程、物理学和气象学等许多不同学科中的多元数据。虽然本质上是一种多元统计方法，但 ICA 的主要发展来自统计领域之外。为 ICA 开发的方法假定多变量数据有些专门的模型。然而，这些方法往往具有一些天然的稳健性，因此通常用于探索性数据分析，特别是聚类分析或无监督学习。 目前，ICA 方法的统计特性尚不清楚。因此，本研究的一个目标是对 ICA 方法的统计和鲁棒性特性进行研究。本研究的另一个目标是研究 ICA 方法作为通用多元统计方法的使用，而不是简单地作为 ICA 问题的解决方案。 为了实现这一目标，将引入和开发一种新的 ICA 方法的无模型解释以及这些方法的一些扩展。首席研究员将这种无模型方法称为不变坐标选择（ICS）。所提出的研究应该对许多使用 ICA 模型的科学和工程学科产生影响，通过提供对其方法的更好的统计理解，从而改进方法和方法。应用程序。 例如，ICA 模型的一个重要应用是解析复杂的信号或源。拟议的研究还将有助于引起一般统计研究界对这些重要统计问题的进一步关注。此外，预计ICS方法的拟议引入和发展将为探索和分析多元数据提供重要且可能非常流行的新方法，也许类似于主成分分析或判别分析的重要性。这些更通用的 ICS 方法不仅应该在统计界产生影响，而且应该在通常处理多元数据的不同学科中产生影响，例如心理学、生物学、地质学等。