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Role of Diversity in ICA and IVA: Theory and Applications

机译:ICA和IVA多样性的作用:理论和应用

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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:独立分量分析(ICA)是解决盲源分离问题的最流行的方法。从简单的线性混合模型和统计独立的假设开始,ICA可以在缩放和排列歧义内恢复一组线性混合源。它已成功应用于众多数据分析问题,以各种各样的生物医学,通信,金融,地球物理学和遥感。可以使用不同类型的分集统计属性实现ICA - 并且可以同时占多种类型的多样性,例如高阶统计,样本依赖性,非圆形度和非间抗性。最近ICA的概括ICA,独立的矢量分析(IVA),将ICA概括为多个数据集,并在数据集中共同实现了多种类型的多样性,统计依赖性的使用,以共同实现多个数据集的独立分解。随着每种新的多样性类型的添加,识别更广泛的信号,并且在IVA的情况下,这包括独立且相同分布的高斯的源。当考虑到多种类型的多样性时,我们审查了ICA和IVA的基本面和性质,然后提出了多样性在实际应用中的重要作用。提出了来自各个域的示例以证明在许多方案中,它可能是一个值得共同占多种统计特性的。本文与2016年SPIE会议的“无监督学习和ICA先驱奖”提供的谈话提交了关于生物医学和认知应用的传感和分析技术的“无监督学习和ICA先驱奖”。

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