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

独立分量分析(ICA)是计算机视觉、心理学、电气工程、物理学和气象学等多个学科中分析多变量数据的一种日益流行的方法。虽然本质上是一种多变量统计方法，但ICA的主要发展来自统计领域之外。为独立成分分析开发的方法假定多变量数据有一定的专门化模型。然而，这些方法往往具有一些自然的稳健性，因此，通常被用于探索性数据分析，特别是用于聚类分析或无监督学习。目前，独立分量分析方法的统计性质还不是很清楚。因此，拟议研究的一个目标是对独立分量分析方法的统计和稳健性进行研究。拟议研究的另一个目标是研究ICA方法作为一般多变量统计方法的使用，而不是简单地作为ICA问题的解决方案。为了实现这一点，将引入和发展一种新的独立成分分析方法的无模型解释，以及这些方法的一些扩展。主要研究人员将这种无模型的方法称为不变坐标选择(ICS)。所提出的研究将对许多使用ICA模型的科学和工程门徒产生影响，因为它提供了对其方法的更好的统计理解，从而导致改进的方法和应用。例如，ICA模型的一个重要应用是解开复杂的信号或信号源。拟议的研究还将有助于提请一般统计研究界进一步注意这些重要的统计问题。此外，预计拟议的ICS方法的引入和发展将为探索和分析多变量数据提供重要的、可能非常受欢迎的新方法，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，而且应该在不同的学科中产生影响，例如心理学、生物学、地质学和其他常规处理多变量数据的学科。

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.