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Role of Diversity in ICA and IVA: Theory and Applications

机译：多样性在ICA和IVA中的作用：理论与应用

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Independent component analysis (ICA) has been the most popular approach for solving the blind source separation problem. Starting from a simple linear mixing model and the assumption of statistical independence, ICA can recover a set of linearly-mixed sources to within a scaling and permutation ambiguity. It has been successfully applied to numerous data analysis problems in areas as diverse as biomedicine, communications, finance, geophysics, and remote sensing. ICA can be achieved using different types of diversity-statistical property-and, can be posed to simultaneously account for multiple types of diversity such as higher-order-statistics, sample dependence, non-circularity, and nonstationarity. A recent generalization of ICA, independent vector analysis (IVA), generalizes ICA to multiple data sets and adds the use of one more type of diversity, statistical dependence across the data sets, for jointly achieving independent decomposition of multiple data sets. With the addition of each new diversity type, identification of a broader class of signals become possible, and in the case of IVA, this includes sources that are independent and identically distributed Gaussians. We review the fundamentals and properties of ICA and IVA when multiple types of diversity are taken into account, and then ask the question whether diversity plays an important role in practical applications as well. Examples from various domains are presented to demonstrate that in many scenarios it might be worthwhile to jointly account for multiple statistical properties. This paper is submitted in conjunction with the talk delivered for the "Unsupervised Learning and ICA Pioneer Award" at the 2016 SPIE Conference on Sensing and Analysis Technologies for Biomedical and Cognitive Applications.
机译：独立成分分析（ICA）是解决盲源分离问题的最流行方法。从简单的线性混合模型和统计独立性的假设开始，ICA可以将一组线性混合的源恢复到缩放和置换模糊度内。它已成功应用于生物医学，通信，金融，地球物理和遥感等领域的众多数据分析问题。 ICA可以使用不同类型的多样性统计属性来实现，并且可以同时考虑多种类型的多样性，例如高阶统计，样本依赖性，非循环性和非平稳性。 ICA的最新泛化，即独立向量分析（IVA），将ICA泛化为多个数据集，并增加了使用另一种类型的多样性，跨数据集的统计依赖性，以共同实现多个数据集的独立分解。通过添加每种新的分集类型，可以识别更广泛的信号类别，就IVA而言，这包括独立且分布均匀的高斯信号源。当考虑多种类型的多样性时，我们回顾了ICA和IVA的基本原理和特性，然后提出一个问题，即多样性在实际应用中是否也起着重要作用。给出了来自各个领域的示例，以证明在许多情况下，可能有必要共同考虑多个统计属性。本文是与2016年SPIE生物医学和认知应用传感和分析技术会议上为“无监督学习和ICA先锋奖”而发表的演讲同时提交的。

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